Preheat oven to 350°F. Line an 8-inch square baking dish with parchment paper and spray with nonstick cooking spray.
In a medium saucepan, melt the butter over medium-low heat. As the butter melts, it’ll start to foam, then turn a clear golden color. Continue to stir the butter, scraping up any browned specks from the bottom of the pan as it starts to brown. It should have a nutty aroma.
Once browned and nutty, turn off the heat. Working relatively quickly so the butter doesn't continue browning from the residual heat in the pan, whisk in chopped chocolate until melted and smooth. Set aside to cool slightly.
Add both sugars to the butter mixture and whisk vigorously until combined. Allow to cool until just barely warm.
Add the eggs, yolk, and vanilla, and whisk until smooth.
Using a rubber spatula, stir in the flour, cocoa powder, salt and espresso powder until just combined. Fold in the chopped cookies.
Pour half of the batter into the baking pan. Dollop teaspoonfuls of half of the Biscoff spread evenly on top, then swirl with a knife. Pour the rest of the batter on top, followed by dollops of the rest of the Biscoff spread, and swirl once again with a knife.* Press the broken Biscoff cookies into the top of the brownies.
Bake for 37-42 minutes, or until brownies look set, and there's no jiggle in the center when you gently wiggle the pan. Allow to cool in the pan for at least 2 hours** before slicing and serving.