Line a baking sheet with parchment paper. Place tablespoon-sized mounds of chocolate-hazelnut spread on the parchment paper. Freeze completely, 2 to 3 hours.
Preheat the oven to 350 degrees F (175 degrees C). Spray an 8-inch-square baking pan with cooking spray.
Combine butter and chocolate chips in a saucepan over medium heat. Cook and stir until mixture is completely melted, 3 to 5 minutes.
Pour chocolate mixture into a bowl and let cool for 5 minutes. Add sugar; mix until dissolved. Add eggs 1 at a time, mixing fully after each addition. Add cream, vanilla extract, baking powder, and salt; mix well. Add flour by spoonfuls, mixing fully after each addition. Pour half the batter into the prepared baking pan. Arrange frozen chocolate-hazelnut mounds on top; cover with remaining batter.
Bake in the preheated oven until top is dry and edges have started to pull away from the sides of the pan, 30 to 40 minutes. Slide a spatula around edges to release sides and let pan cool fully on a rack or countertop, at least 30 minutes. Cover with plastic wrap and refrigerate until set, about 2 hours. Cut into squares.