Heat oven to 350°F. Line a 9-inch square pan with parchment, leaving overhang.
Melt the butter gently and let it cool for 5 minutes.
Whisk in granulated and brown sugars until combined and grainy.
Stream in beaten eggs and vanilla, whisking until glossy and thick.
Stir together flour, cocoa, salt, and espresso powder in a small bowl.
Fold the dry mixture into the wet just until no dry streaks remain.
Stir in 3/4 cup chocolate chips and 3/4 cup walnuts.
Spread the batter evenly in the prepared pan.
Bake for about 27 minutes, until edges are set and the center is just slightly soft.
Scatter marshmallows, remaining chocolate chips, and remaining walnuts over the hot brownies.
Return to the oven for 4–5 minutes, until the marshmallows puff and lightly toast.
Cool completely in the pan, then lift out, slice, and serve.