Preheat oven to 350 degrees. Grease a 8x8 baking dish and set aside.

In the bowl of a stand mixer, whisk together 1/2 cup melted butter and granulated sugar. Mix until light and fluffy.

Add in eggs, one at a time, allowing each to be fully incorporated.

Pour in 1 teaspoon vanilla extract and continue mixing for 30 seconds.

Combine flour, 1/3 cup cocoa powder, salt, and baking powder in a bowl and mix.

Working in batches, slowly add dry ingredients to wet ingredients. Mix batter well after each addition.

Fold in the chocolate chunks.

Pour batter into greased baking dish using a rubber spatula.

Bake uncovered for 30 minutes.

Combine the powdered sugar, 1/4 cup softened butter, milk, 3 tablespoons cocoa powder, and 1 teaspoon vanilla to the bowl of a stand mixer.

Beat, 2 minutes, until light and fluffy.

Spread frosting on brownies while still hot.

Let brownies fully cool before serving. Store any uneaten brownies in the refrigerator.