Preheat the oven to 350°F. Line a baking sheet with parchment paper.
In a skillet set over medium heat, add 1 cup raw pecans and 2 tablespoons real maple syrup. Cook, stirring often, until the pecans are toasted and golden and the syrup has mostly cooked down, about 5–8 minutes. Transfer the pecans to a cutting board, sprinkle with flakey sea salt, cool completely, then roughly chop.
In a clean skillet set over medium heat, add 1 stick butter. Cook, stirring or swirling frequently, until the butter foams and the milk solids turn golden brown and smell nutty, about 2–3 minutes. Remove from the heat and let the browned butter cool until warm or room temperature.
In a large mixing bowl, beat together the remaining 1 stick butter (at room temperature), the cooled browned butter, 3/4 cup dark brown sugar, and 1/3 cup granulated sugar until combined and slightly fluffy.
Beat in 2 eggs and 1 tablespoon vanilla extract until the mixture is creamy.
Add 2 1/4 cups all-purpose flour and 1 teaspoon baking soda to the bowl and mix until just combined; avoid overmixing.
Stir in 2 cups semi-sweet chocolate chips and the chopped pecans.
Roll the dough into tablespoon-size balls and place them about 3 inches apart on the prepared baking sheet.
Bake at 350°F for 8–10 minutes, until the edges are just beginning to set but the centers are still soft. Remove from the oven and let the cookies cool on the baking sheet for 5 minutes (they will continue to cook slightly), then transfer to a wire rack.
If desired, sprinkle tops with coarse sugar while the cookies are still warm. Store cooled cookies in an airtight container for up to 4 days.