Preheat the oven to 350°F (180°C). Lightly coat a 9-inch (23 cm) springform pan with nonstick cooking spray.
In a medium saucepan set over medium heat, melt ½ cup (113.5 g) unsalted butter. Remove the pan from the heat, add 3½ ounces (99.22 g) finely chopped dark chocolate, let sit for about 30 seconds, then whisk until smooth and glossy.
Whisk in 1⅓ cups (293.33 g) lightly packed light brown sugar, 1 teaspoon vanilla extract, and ½ teaspoon instant espresso powder until fully combined and smooth.
Whisk in the 3 room-temperature eggs, one at a time, scraping the sides of the pan as needed so each egg is fully incorporated before adding the next.
Sprinkle in ½ cup (62.5 g) all-purpose flour, 1 teaspoon baking powder, and ½ teaspoon salt. Use a rubber spatula to fold the dry ingredients into the batter until no streaks of flour remain.
Spread the batter evenly into the prepared springform pan and bake for 20–25 minutes, or until the cake has puffed slightly and the top is shiny and just barely cracked.
Transfer the pan to a wire rack and cool completely before removing the sides of the springform pan.
While the cake cools, make the frosting: in a large bowl, use an electric mixer on medium speed to beat ¾ cup (177.44 g) speculoos cookie butter and 6 tablespoons unsalted butter (at room temperature) for 1 minute, until light and fluffy. Scrape down the bowl as needed.
Add ⅔ cup (80 g) powdered sugar, ¼ teaspoon salt, and 2 tablespoons heavy whipping cream to the bowl. Beat on medium speed for about 1 minute, or until the frosting is fluffy and spreadable. Scrape the bowl to ensure everything is well combined.
Spread the frosting over the completely cooled brownie cake, garnish with chocolate shavings, and cut into wedges to serve.
Store leftovers covered at room temperature for up to 3 days or in the refrigerator for up to 5 days.