Preheat the oven to 325°F. Heat the oven to 325°F and spread 1 1/4 cups pecan halves in one loose layer. Toast them for 7 to 9 minutes. Shake the pan at minute 4 so the outer pieces move toward the center. Cool the nuts for 5 minutes. Then reserve 12 attractive halves and chop the rest into irregular pea-sized pieces. The pecans should deepen from tan to light amber and smell warm and woody. Their ridges will look dry rather than oily. Pull them immediately when that aroma appears because an extra 2 minutes can make their natural oils taste bitter. Toast at 325°F because gentle heat deepens flavor without scorching the pecan oils.

Melt 12 tablespoons unsalted butter over medium heat at about 5 on a 10-dial. Cook it for 5 to 7 minutes. Swirl the pan every 30 seconds and scrape the bottom gently so the milk solids don't stick. Remove it when the butter reaches deep amber. Then cool it for 15 minutes until it falls near 95°F. The foam will rise and then thin as chestnut-brown flecks collect underneath. You'll hear the loud bubbling soften and smell toasted hazelnuts. (My first batch used hot butter, the dough turned greasy and spread too far.) Go past dark amber and the milk solids burn. Cooling to 95°F keeps the egg from warming and protects the dough structure.

Keep the ingredients between 68°F and 72°F. Whisk the browned butter with dark brown sugar and granulated cane sugar for 45 seconds. Add the large egg, egg yolk and pure vanilla extract. Whisk for another 30 seconds. Then fold in the flour mixture with 12 to 15 broad strokes before adding the chopped toasted pecans. The Butter Pecan Cookies dough should look thick and glossy with visible sugar grains and pecan pieces. Drag a spatula through the center and the groove should close slowly. Stop once no dry flour pockets remain because extra folding builds too much gluten. Fold briefly because limited gluten keeps the baked centers tender instead of bread-like.

Divide the dough into 12 portions weighing about 55 grams each. Roll each portion only twice between your palms so the surfaces stay slightly rough. Place six mounds on each lined baking sheet with 3 inches between them. Press one reserved pecan half into every mound. Chill the trays at 38°F for 30 to 45 minutes. The chilled mounds should feel firm around the base but slightly yielding on top. Their pecan halves should remain exposed and the dough shouldn't look wet. Skip the chill and the butter melts before the flour network sets, which produces thin cookies. Chilling firms the butter so the centers stay thick during the first baking minutes.

Heat the oven to 350°F and place the chilled trays on the upper-middle and lower-middle racks. Bake for 11 to 13 minutes. At minute 7 rotate each tray and swap their rack positions. Remove the cookies when the edges turn amber but the centers still look slightly pale. Sprinkle flaky sea salt over them within 30 seconds. The surfaces should appear craggy with a soft central rise and darker rings around the edges. A few pecan ridges may glisten from their oils. Cool the cookies on their trays for 10 minutes because moving them sooner can split the tender centers. Pull at pale centers because residual heat finishes setting them without drying the crumb.

Thick round bakery-style cookies with gently craggy edges and slightly domed centers. Each cookie is about 3 1/2 inches wide and 1/2 inch thick, filling roughly one palm. whole pecan halves pressed into the tops. chopped toasted pecans visible through the dough. pale golden centers with deeper amber edges. irregular homemade circles rather than identical discs. One cookie has a rough front break that reveals a soft dense crumb with embedded toasted pecan pieces. Matches step 5 except one cookie has transferred to a plate and its interior is now visible.