Brown the butter. Place the butter (1 cup) in a heavy-bottomed medium saucepan and melt over low heat. Once melted, increase the heat to medium and cook, stirring occasionally, until the milk solids turn golden brown and the butter smells nutty. Watch closely — it can burn quickly. Remove from heat and let cool for 20 minutes.
Mix the dry ingredients. In a medium bowl, whisk together the bread flour (2 1/4 cups), salt (1 teaspoon), and baking soda (1 teaspoon). Set aside.
Cream the butter and sugars. Add the cooled brown butter to the bowl of a stand mixer, fitted with the paddle attachment. Add both sugars (1/4 cup sugar + 1 1/4 cups brown sugar) and beat on medium for 3 minutes.
Add the egg, yolk, cream, and vanilla. Mix in the egg (1) and egg yolk (1) just until combined. Add the heavy cream (2 tablespoons) and vanilla (2 teaspoons) and beat on medium for another 3 minutes.
Add the dry ingredients. Slowly add the flour mixture, mixing on low after each addition. Once incorporated, mix briefly on medium to fully combine.
Add the mix-ins. Fold in the pretzels (1/2 cup), chocolate chips (1/2 cup), and butterscotch chips (1/2 cup) until evenly distributed.
Scoop the dough. Line a baking sheet with parchment. Scoop dough into tablespoon-size balls (slightly smaller than a golf ball). The dough may look crumbly — simply press and shape it with your hands to form smooth balls.
Chill the scooped dough. Refrigerate the dough balls on the baking sheet overnight.
Prep. Arrange the oven rack to the center (middle) position and preheat the oven to 350°F (177ºC). Line baking sheets with parchment or Silpats.
Bake. Place chilled dough balls 2 inches apart on the prepared sheets and gently flatten the tops slightly. Bake for 8–12 minutes, until the edges are set and the centers appear slightly underbaked. (11 minutes is my sweet spot!)
Cool. Let the cookies rest on the baking sheet for 10 minutes, then transfer to a cooling rack.