Heat the 10-inch skillet over medium-high heat, about 7 on a 10-dial, for 2 minutes. Slice 6 small yellow patty pan squash into 24 uneven 1/4-inch rounds. Thinly slice 1 small yellow onion into about 20 arcs. Add the extra-virgin olive oil and 1/4 teaspoon kosher salt. Spread everything in one loose layer. Cook for 8 to 10 minutes and turn the pieces every 2 minutes. The squash should lose its chalky center and pick up amber spots around the scalloped edges. Meanwhile, the onion turns soft and smells lightly sweet. Stop when the skillet looks almost dry. Go past 12 minutes and the smallest slices collapse. Pull it sooner and trapped water loosens the eggs later. Browning first removes moisture and concentrates the squash flavor.

Lower the heat to medium, about 5 on a 10-dial. Add 2 minced garlic cloves and 2 packed cups baby spinach to the same skillet. Fold the greens through the hot squash for 90 seconds to 2 minutes. Rotate the skillet halfway through so the back edge doesn't cook faster. Keep the squash pieces visible instead of burying them under the spinach. You'll smell toasted garlic just as the spinach darkens and shrinks to about one-third of its volume. The leaves should look glossy but no green liquid should pool underneath. Cook beyond 3 minutes and the garlic tastes bitter. Stop too soon and the spinach leaks water during baking. Brief wilting protects the egg mixture from excess moisture.

While the vegetables cool for 3 minutes off the heat, keep the oven at 375°F. Crack 8 large eggs into a large bowl and whisk for 45 seconds using quick side-to-side strokes. Add whole milk and the remaining 1/2 teaspoon kosher salt and black pepper. Fold in sharp cheddar and Parmigiano-Reggiano and fresh thyme for another 20 seconds. Scrape the bowl once so no dense egg streaks remain. The mixture should look pale gold and lightly foamy with cheese suspended throughout. Stop whisking when the whites disappear but before the foam becomes thick. Overwhisking for more than 90 seconds traps too much air and causes a puffy top that sinks. Underwhisking leaves rubbery white patches. Short mixing builds an even curd without making the frittata spongy.

Return the skillet to medium-low heat, about 4 on a 10-dial. Redistribute the squash and spinach so bare spaces remain between pieces. Pour the egg mixture slowly from center to edge and tilt the skillet twice. Cook without stirring for 4 to 5 minutes. Run a spatula around the rim once at minute 3 so the setting edge doesn't stick. The rim should turn opaque while the center stays loose and glossy. Small bubbles may appear near the cheese but the surface shouldn't boil. (I used to rush this step - the center slid under the vegetables when sliced.) Cook longer than 6 minutes and the bottom toughens before baking. A partly set rim anchors the vegetables and supports clean slices.

Transfer the skillet to the 375°F oven and bake for 12 to 16 minutes. Check at minute 12 by nudging the center. It should wobble once as a single soft mass. Continue until an instant-read thermometer reaches 160°F at the center. Rotate the skillet 180 degrees at minute 8 if your oven browns unevenly. Don't wait for the middle to become rigid. The edges should puff slightly and show deep golden freckles from the cheddar and Parmigiano-Reggiano. The middle stays moist but no wet egg should shimmer when tilted. Pull it after 165°F and the curds tighten and squeeze out moisture. Remove it below 160°F and the center may remain unsafe. Moderate oven heat sets the center before the edges turn rubbery.

Rest the skillet off the heat until the center drops to about 145°F, usually 5 minutes. Sprinkle 1 tablespoon fresh dill across the top and cut the frittata into 4 uneven wedges. Slide one wedge onto a white plate with the browned top facing upward. Let the slice stand for 2 minutes before serving so steam can escape without soaking the base. The wedge should hold clean edges while the center stays tender and speckled with squash and spinach. A few cheese strands may stretch near the cut and the top should look patchy rather than uniform. Slice immediately and the center tears. Wait longer than 15 minutes and the surface loses its gentle warmth. Resting lets the egg proteins settle without squeezing out moisture.