Melt the butter in a light-colored saucepan over medium heat, swirling often, for 5 to 7 minutes, until it foams and turns golden brown with a nutty aroma. Pour it into a large bowl, scraping in all the browned bits, and cool for 15 minutes.
Blend the cottage cheese until completely smooth. Whisk the brown sugar into the cooled brown butter, then whisk in the blended cottage cheese, egg yolk and vanilla until glossy.The cottage cheese replaces the moisture lost while browning the butter, which keeps these cookies soft and chewy in the center.
Stir in the flour, protein powder, baking soda and salt until just combined, then fold in two thirds of the toffee bits. Cover and chill the dough for 30 minutes.
Preheat the oven to 350°F and line 2 baking sheets with parchment paper. Scoop the dough into 2 tablespoon balls, place them 2 inches apart and press the remaining toffee bits onto the tops.
Bake for 10 to 12 minutes, until the edges are golden and the centers look slightly underdone. Sprinkle with flaky sea salt as soon as they come out of the oven.
Cool on the baking sheets for 10 minutes to set, then move to a wire rack.