Heat the oven to 425°F. Halve 3 medium garnet sweet potatoes lengthwise and place them cut side down on a parchment-lined rimmed sheet pan. Roast for 40 to 50 minutes. Rotate the pan at minute 25 so the edges color evenly. Let the halves rest for 10 minutes until the centers cool to about 110°F. The skins should wrinkle and pull from the flesh. The cut sides will show dark amber spots and the centers should smell sweet and nutty. A knife should slide through without resistance. Pull them early and the mash stays firm and lumpy. Go past 55 minutes and the edges dry into tough bits. Roast at 425°F because dry heat concentrates starch without adding water.

Scoop 3 roasted garnet sweet potatoes into a large bowl while the flesh is near 110°F. Press until no firm pieces remain. Add 1 large egg yolk, 1/4 cup finely grated Parmigiano-Reggiano, 1 teaspoon Diamond Crystal kosher salt and 1/4 teaspoon ground nutmeg. Fold in 1 1/2 cups 00 flour with a rubber spatula for about 90 seconds. Then press the mixture together with your fingertips for 30 to 45 seconds. Stop when one soft orange mass forms and only a few flour streaks remain. It should feel tacky but shouldn't glue itself to your hand. (My first batch got a full five-minute knead, it turned bouncy and dense.) Overmix and the dough becomes chewy. Fold briefly because excess gluten makes the gnocchi tough.

Dust a large wooden cutting board with 1/4 cup 00 flour. Divide the orange dough into 4 uneven pieces. Roll each piece into a rope about 3/4 inch thick using light outward strokes. Cut the ropes into 36 squat pillows about 1 inch long. Press shallow ridges into one side and keep the pieces loosely spaced for 12 to 15 minutes. Move the 36 shaped gnocchi to a floured tray and chill at 40°F for 10 minutes. The ridges should stay visible and the corners should look softly rounded rather than sharp. If the pieces slump before chilling, dust them with 1 tablespoon more flour. Warm dough spreads and loses its ridges. Chill 10 minutes because firmer starch keeps the pillows intact.

Bring 4 quarts filtered water and 1 tablespoon Diamond Crystal kosher salt to a full 212°F boil in a 6-quart pot. Lower 12 chilled gnocchi into the water at a time. Stir once from the bottom after 20 seconds. Cook for 2 to 3 minutes until every piece floats, then give them 30 seconds more. Lift each batch out and let excess water drain for 20 seconds. The orange pillows should look slightly deeper in color with swollen ridges and a smooth damp surface. You'll hear the boil return within 30 seconds after each batch enters. Crowding all 36 pieces drops the temperature and makes their surfaces gummy. Boil in batches because steady heat sets the flour without waterlogging.

Heat 2 tablespoons extra-virgin olive oil in a 12-inch cast-iron skillet over medium-high heat at about 7 on a 10-dial for 90 seconds. Add 8 ounces sliced cremini mushrooms in one loose layer. Leave them untouched for 3 minutes. Flip and cook for 3 more minutes until their edges turn dark brown and their centers shrink. Lower the heat to medium at about 5 on a 10-dial. Add 4 tablespoons unsalted European-style butter, 2 minced garlic cloves, 1 tablespoon chopped rosemary, 1 tablespoon chopped sage, 1/3 cup walnut halves and 1/3 cup sliced oil-packed sun-dried tomatoes. Stir for 90 seconds. The butter should foam and smell nutty. Go longer and the garlic turns bitter. Brown the butter gently because milk solids scorch fast.

Raise the skillet to medium-high heat at about 6 on a 10-dial. Add 18 boiled gnocchi and spread them into one loose layer. Leave them untouched for 2 minutes, then flip and cook for 2 more minutes. Move that batch to a plate and repeat with the remaining 18 pieces. Return all 36 gnocchi to the skillet. Toss for 60 seconds so the amber butter and herbs coat every piece. Add 1/4 teaspoon freshly ground black pepper and 2 tablespoons Parmigiano-Reggiano. The gnocchi should show irregular deep golden patches while their orange centers stay soft. (I used to stir constantly, the color never developed.) Move too often and the crust can't form. Leave each side still because direct contact creates caramelized edges.

Divide the skillet mixture into 4 portions while it remains near 150°F. Place 9 gnocchi in each small pale blue-gray ceramic pasta bowl. Spoon the cremini mushrooms, walnut pieces and sun-dried tomato strips between the pillows rather than over them. Finish each bowl with 1/2 tablespoon finely grated Parmigiano-Reggiano and 1/4 teaspoon each fresh rosemary and sage. Serve within 3 minutes. The butter should still look glossy and the Parmesan should soften without disappearing. Each bowl needs uneven overlap and a mix of orange and deep golden surfaces. Wait 10 minutes and the butter starts to firm around the edges. Don't bury the gnocchi under garnish because their browned patches should remain visible. Plate while hot because warm butter carries the herb aroma.