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Lightly grease (or line with parchment) two baking sheets.
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Place half the butter (8 tablespoons, 113g) in a medium skillet. Melt the butter over medium heat, swirling it in the pan occasionally. It'll foam and froth as it cooks, and start to crackle and pop. Once the crackling stops, keep a close eye on the melted butter, continuing to swirl the pan at intervals. The butter will become fragrant, and brown bits will form in the bottom. Once the bits are amber brown (about 2 1/2 to 3 minutes or so after the sizzling stops), remove the butter from the burner and pour it into a small bowl, bits and all. Allow it to cool for 20 minutes.
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Beat the remaining 8 tablespoons (113g) butter with the brown sugar for 3 to 5 minutes, until the mixture is very smooth.
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Beat in the vanilla and molasses.
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Pour the cooled brown butter into the bowl, along with the granulated sugar. Beat for 2 minutes, until smooth; the mixture will lighten in color and become fluffy.
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Add the egg and egg yolk, and beat for another minute.
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Add the flour, salt, and baking soda, beating on low speed just until everything is incorporated.
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Use a spatula to fold in the chocolate chips and pecans.
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Scoop the dough onto a piece of parchment paper, waxed paper, or plastic wrap. Flatten it slightly into a thick disk, and refrigerate for at least 30 minutes. About 15 minutes before you're ready to begin baking, preheat your oven to 350°F, with the racks in the center/upper third.
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Scoop the dough in 2 tablespoon-sized (28g) balls onto the prepared baking sheets. Leave about 2" between the cookies; they'll spread as they bake.
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Sprinkle the cookies with sea salt, to taste — as much or as little as you like.
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Bake the brown butter chocolate chip cookies for 12 to 15 minutes, until they're golden brown. Remove them from the oven, and allow them to rest on the baking sheet for at least 5 minutes before moving them.
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Serve the brown butter chocolate chip cookies warm; or cool completely, and store airtight at room temperature for several days. For longer storage, wrap well and freeze.
