Preheat the oven to 325°F. Line the bottom of an 8-inch square baking pan with parchment paper and liberally coat the paper and the pan sides with flavorless vegetable oil.

Put 3 ounces of the chocolate and the butter in a medium stainless-steel bowl and set over a pot of simmering water. Heat, stirring occasionally, until the chocolate and butter melt and are fully combined and the mixture is smooth. Lift the bowl from the pot. Set aside.

Sift the flour and salt together into a bowl. In another bowl, combine the eggs and vanilla extract and whisk together by hand until blended. Whisk in the sugar.

Whisk the egg mixture into the chocolate. Add the flour and the remaining 2½ ounces chocolate to the batter and, using a rubber spatula, mix well. Then mix in the walnuts.

Pour the batter into the prepared pan. Spread it evenly with a small offset spatula. Scatter the marshmallow pieces evenly over the surface and push them halfway into the batter. The tops should remain uncovered.

Bake on the middle shelf of the oven until the marshmallows are browned and a skewer inserted into the center of the brownie sheet comes out with some batter clinging to it, about 45 minutes. Let cool completely in the pan on a wire rack, then cover with plastic wrap and refrigerate until cold.

Run a table knife around the edge of the pan to loosen the sides of the brownie, and then slide the brownie, still on the paper, onto a work surface. Using a ruler to guide you and a sharp knife, cut into sixteen 2-inch squares. Store in an airtight container in the refrigerator for up to 3 weeks.