Preheat the oven to 350 degrees F.
Spread the chopped walnuts on a baking pan; toast until fragrant, 5 to 10 minutes. Transfer nuts to a bowl to cool.
Increase oven temperature to 400 degrees F.
Line a 9 by 13-inch baking pan with parchment paper and generously butter; set aside.
Combine the unsweetened chocolate and butter in a heatproof bowl or the top of a double boiler. Set over a pan of simmering water until mixture has melted. Remove from heat; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat the eggs, sugar, and espresso at high speed until light and fluffy, about 5 minutes. Reduce speed to low, and add the melted chocolate mixture and the vanilla; beat until combined. Slowly add the flour and salt; beat just until incorporated. Fold in the chopped chocolate and toasted walnuts. Pour into prepared pan.
Bake until edges are dry but center is still soft, about 35 minutes. Remove from oven. In a medium bowl, combine chopped walnuts, chocolate chunks, and marshmallows. Sprinkle evenly over brownies to cover.
Return to oven and continue to bake until the chocolate is partially melted and the marshmallows are soft and very lightly browned, about 5 minutes. Transfer to a rack and let cool for 20 minutes. Using a serrated knife, cut into 8 squares; serve warm or at room temperature. Store in an airtight container for up to 2 days.