Line an 8-inch square pan with a parchment sling. Preheat the oven to 325°F (163°C).
Brown the butter: In a small saucepan over medium heat, cook the butter until the milk solids turn deep golden and it smells nutty, 4–6 minutes. Immediately pour into a mixing bowl to cool slightly.
Melt the chocolate gently in the microwave in short bursts or over a double boiler until smooth; let it cool to warm, not hot.
Whisk the sugar into the warm browned butter until glossy. Add the eggs and yolk one at a time, whisking vigorously after each for about 30 seconds, then whisk in the vanilla and melted chocolate until the mixture is thick and shiny.
In a separate bowl, whisk together the flour, cocoa, salt, baking powder, and espresso powder. Fold the dry ingredients into the chocolate mixture just until no dry spots remain. Let the batter rest for 10 minutes to hydrate the cocoa.
Scrape the batter into the prepared pan and smooth the top. Bake for 25–30 minutes, until the edges are set and a toothpick inserted toward the center shows a few moist crumbs. Cool in the pan on a rack for 30 minutes, then chill for 20 minutes for easier layering.
Make the mint cream: Beat the softened butter on medium-high until creamy, about 1 minute. Mix in half the powdered sugar, then the cream and peppermint extract. Beat in the remaining sugar until pale, fluffy, and spreadable, 2–3 minutes. Spread evenly over the cooled brownie layer. Chill 10 minutes to firm up.
Prepare the glaze: Heat the cream in a small saucepan until steaming (do not boil). Pour over the chopped chocolate and corn syrup in a bowl; let stand 2 minutes, then stir from the center outward until silky. Cool 5–10 minutes until slightly thickened but still pourable.
Pour the glaze over the mint layer and tilt the pan to coat. Tap to release bubbles. Chill 30–40 minutes until set but not rock hard. Lift out with the parchment and slice with a warm, dry knife, wiping between cuts.