Brown the butter: In a medium saucepan over medium heat, melt the butter (1 cup + 3 tablespoons). Add powdered milk (2 tablespoons) and cook, stirring constantly, scraping the edges and bottom of the saucepan, to prevent the milk solids from burning. Cook until milk solids turn deep golden brown and smell nutty. Immediately transfer to a heatproof bowl and cool until just warm. Mix sugars: Stir brown sugar (3/4 cup) and granulated sugar (1/2 cup) into the browned butter. Let cool slightly.
Add eggs: Whisk in eggs (2), egg yolks (2), vanilla (1 tablespoon), and molasses (2 teaspoons) until smooth and glossy.
Combine dry ingredients: In a separate bowl, whisk together all-purpose flour (1 1/2 cups), bread flour (3/4 cup), cornstarch (1 1/2 teaspoons), baking soda (1 teaspoon), and salt (1 1/2 teaspoons).
Make dough: Add dry ingredients and chocolate chips to the wet ingredients. Fold just until combined.
Portion dough: Scoop into 50–51g portions (about a #24 scoop).
Stuff marshmallows: Flatten each dough portion slightly. Place 3–4 mini marshmallows in the center, then wrap the dough around them and seal completely.
Chill: Place dough balls on a tray and refrigerate for at least 2 hours, or up to 48 hours.
Bake: Preheat oven to 370°F (188ºC). Bake cookies for 7–8 minutes, until edges are set and lightly golden but centers remain soft.
Shape + finish: Immediately shape cookies if needed using a round cutter or spatula. Sprinkle with flaky salt.
Cool: Let cookies cool completely on the baking sheet to set centers while keeping them soft and gooey.