How to Make It
Melt butter in a small skillet over medium heat. Continue to cook, swirling occasionally, until butter is golden and nutty smelling, about 3 minutes. Transfer to a large bowl and let cool slightly. Whisk both flours, kosher salt, and baking soda in a medium bowl.
To butter, add both sugars and stir vigorously with a wooden spoon (really go for it) until evenly incorporated and slightly thickened, about 1 minute. Add egg and vanilla and stir until silky looking, 30 seconds or so. Add flour mixture and stir to combine. Fold in butterscotch and chocolate. Refrigerate dough 15 minutes (this will keep the cookies from spreading too much).
Preheat oven to 375°F with racks in upper and lower thirds. Line two baking sheets with parchment paper. Roll or scoop dough into 1 ½-inch balls and place 3 inches apart on prepared sheets. Sprinkle with flaky sea salt and bake, rotating sheets from top to bottom halfway through, until golden on the edges but still soft in the center, about 10 minutes. Let cool slightly, but not too much because these are really divine eaten warm.