Prepare the Base:

1. Preheat the Oven: Preheat the oven to 350°F (175°C). Grease and line an 8×8-inch square baking pan with parchment paper.
2. Mix the Dry Ingredients: In a medium bowl, whisk together the flour, cocoa powder, baking powder, and salt. Set aside.
3. Cream the Butter and Sugar: In a large mixing bowl, beat the softened butter and granulated sugar together until light and fluffy.
4. Add the Eggs and Vanilla: Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
5. Combine Wet and Dry Ingredients: Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
6. Melt the Chocolate: In a small saucepan, heat the heavy cream over low heat until warm. Add the chocolate chips and stir until fully melted and smooth.
7. Add the Chocolate to the Batter: Fold the melted chocolate into the batter, ensuring an even distribution.
8. Bake the Base: Pour the batter into the prepared baking pan and spread it evenly. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean. Let cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.

Prepare the Frosting:

9. Mix the Frosting Ingredients: In a medium bowl, whisk together the powdered sugar, cocoa powder, softened butter, and vanilla extract. Gradually add the milk, a tablespoon at a time, until you achieve a smooth, spreadable consistency.
10. Frost the Chocolate Velvets: Once the base is completely cooled, spread the frosting evenly over the top using a spatula.

Serve and Garnish:

11. Cut into Squares: Once the frosting has set, cut the chocolate velvet into squares or bars.
12. Garnish (Optional): For extra flair, garnish with chocolate shavings, sprinkles, or a dusting of powdered sugar.