Preheat the oven to 350°F (176°C). Line a sheet pan with parchment paper or a nonstick liner. Melt the butter in a large microwave-safe bowl, then let it cool for 5 minutes (hot butter = greasy cookies).
Whisk in both sugars until smooth, about 1–2 minutes. Add the egg, then the yolk and vanilla. Thoroughly whisk until the mixture is smooth and fully emulsifed.
Use a blender to finely crush graham crackers until they resemble flour (see note 1). Spoon crumbs into a measuring cup and level off the top.
Add the graham cracker crumbs, salt, and baking soda to the wet mixture and whisk to combine. Add the flour, milk chocolate chips, and mini chips. Mix with a wooden spoon or electric hand mixer until a thick dough forms and no dry streaks remain.
Scoop dough into 2-tablespoon (40g) portions and roll into smooth balls. IF the dough balls feel warm/greasy and aren't holding shape in a ball, chill for 30–60 minutes; otherwise, bake right away.
Place 6 dough balls, spaced apart, on the prepared sheet pan. Bake for 8 minutes, then remove from the oven. Quickly press 2-3 mini marshmallows and 3–4 chopped chocolate pieces into the tops of each cookie. Return to oven and bake 2 more minutes, or until the edges are lightly golden and the tops are just set (don’t overbake).
Let cookies cool on the pan for 5 minutes before transferring to a wire rack. Repeat with remaining dough or freeze extras (see below).
Video
Notes
Note 1: Use a blender or food processor for fine, even crumbs—larger chunks will mess up the cookie texture. Storage: Store cookies in an airtight container at room temp and enjoy the same day (the marshmallows get stale and harden over time). To freeze, roll dough balls, freeze on a tray until solid, then transfer to a sealed bag or container for up to 3 months. When baking frozen, press them down slightly with the back of a spatula midway through bake time.