Preheat oven to 350°F. Line an 8-inch or 9-inch square metal pan with parchment paper, leaving flaps for easy lifting.

For the brownie batter: Melt the butter and chocolate together in a heat-safe bowl until smooth. Whisk in both sugars while warm, then add eggs one at a time, followed by vanilla. Sift in flour, cocoa powder, salt, and espresso powder if using. Fold just until combined; the batter should be glossy and thick.

For the cookie dough: Beat the softened butter with both sugars until combined and slightly fluffy, about 1 minute. Mix in the egg yolk and vanilla. Sprinkle in flour, baking soda, and salt, stirring just until there are no dry spots. Fold in chocolate chips, then chill the dough in the refrigerator for 10 to 20 minutes.

Spread the brownie batter evenly in the prepared pan. Scoop cookie dough in heaping teaspoon mounds across the surface, leaving a little space between scoops. Lightly swirl a butter knife once or twice to create a marbled effect.

Bake for 22 to 28 minutes for an 8-inch pan or 18 to 24 minutes for a 9-inch pan. Rotate the pan halfway through. Look for set edges and a soft center that gives a gentle jiggle.

Allow the pan to cool on a rack for at least 45 minutes before lifting out and slicing with a warm knife, wiping between cuts for clean edges.