1. Butter, softened - ½ cup
2. Chocolate-hazelnut spread (such as Nutella®), at room temperature - ⅓ cup
3. Cocoa powder, sifted - ⅓ cup
4. Powdered sugar, sifted - 2 cups
5. Vanilla extract - 1 tablespoon
6. Milk, or more as needed - 1 ½ tablespoons