In a light-colored medium saucepan, melt butter over medium-high heat. Cook, stirring frequently, until milk solids have turned a deep amber color and butter is fragrant, 8 to 10 minutes. Pour into a shallow heatproof dish, and let cool at room temperature until solidified.

Preheat oven to 350°F (180°C). Line baking sheets with parchment paper.

In the bowl of a stand mixer fitted with the paddle attachment, beat solidified browned butter (about 170 grams), coconut oil, and sugars at medium speed until fluffy, 2 to 3 minutes, stopping to scrape paddle and bottom and sides of bowl. Add egg and egg yolk, one at a time, beating well after each addition. Beat in vanilla.

In a medium bowl, whisk together flour, baking powder, kosher salt, and baking soda. With mixer on low speed, gradually add flour mixture to butter mixture, beating just until combined. Stir in chocolate chips and coconut.

Using a 3-tablespoon spring-loaded scoop, scoop dough (about 52 grams each), and place 3 inches apart on prepared pans. Using the palm of your hand, slightly flatten dough balls.

Bake until golden brown, 12 to 15 minutes, rotating pans halfway through baking. Garnish with sea salt, if desired. Let cool on pans for 5 minutes. Remove from pans, and let cool completely on wire racks. Store in an airtight container for up to 3 days.