Browned butter gives these a toffee depth that plain melted butter can't, the extra yolk keeps the middles soft, and chilling the dough is what stops them spreading thin.

Brown the butter: melt it in a small saucepan over medium-low heat, scraping the bottom and sides with a silicone spatula every 10 to 15 seconds. It foams first, then the bubbles shrink and it starts to smell nutty. Keep stirring until it turns golden brown with small toasted flecks floating in it, 5 to 7 minutes. Take it off the heat and let it cool in the pan for 10 minutes, or it will scramble the egg.
In a large bowl, stir the brown butter, flecks and all, together with both sugars. Add the egg, the extra yolk and the vanilla and mix until smooth.
Fold in the flour, baking soda and salt just until no dry streaks remain, and stop there. The dough should feel soft but not sticky, giving slightly when you press it.
Fold in the chocolate chips until they're evenly spread, without overworking the dough. Cover and refrigerate for at least 1 hour, or up to overnight.
Heat the oven to 350°F and line two sheet pans with parchment. Let the chilled dough sit at room temperature until it's soft enough to scoop, about 20 minutes.
Portion the dough with a 1½-ounce scoop, about 3 tablespoons each. Roll each ball smooth between your palms and set them 2 inches apart on the pans.
Bake 12 to 13 minutes, until puffed and light golden at the edges but still soft in the middle; they firm up as they cool. Sprinkle with flaky salt straight out of the oven, and let them cool a few minutes on the pans before moving them.
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