Preheat oven to 350°F (175°C). Line a large baking sheet with parchment paper and set aside.

In a medium bowl, sift together 1 1/4 cups all-purpose flour, 1 1/2 teaspoons baking powder, and 1/4 teaspoon sea salt; set the dry mixture aside.

In a small saucepan over medium-low heat, melt 1 stick unsalted butter, whisking constantly, until the butter browns and gives a nutty aroma. Remove the pan from the heat immediately.

Pour the browned butter into a large mixing bowl or the bowl of a stand mixer. Let the butter cool until it is warm but not hot (about 2–5 minutes).

Add 3/4 cup brown sugar and 1 teaspoon vanilla extract to the warm browned butter. Beat by hand or with a mixer on medium speed until the mixture is lighter in color and slightly fluffy, about 2–3 minutes.

Add 1 large room-temperature egg and beat just until the egg is incorporated, about 30 seconds.

Add the sifted dry ingredients to the butter mixture in three additions, mixing on low speed (or folding by hand) and scraping the bowl after each addition. Mix only until the dough is combined and no streaks of flour remain.

Stir in 3/4 cup white chocolate chips and 3/4 cup chocolate toffee bits with a spatula until evenly distributed.

Using a large ice cream scoop (to make 8 large cookies), portion the dough into 8 mounds and place them on the prepared baking sheet, spacing the cookies evenly.

Bake in the preheated oven for 14–15 minutes, rotating the pan halfway through baking for even color, until the edges are set and the tops are lightly golden.

Remove the baking sheet from the oven and let the cookies cool on the sheet for at least 5 minutes, then transfer them to a wire rack to cool completely.

Store cooled cookies in an airtight container for up to 3 days.