Cut 2 sheets of parchment paper that are the same width as the bottom of a 9"x9" pan. Line the pan in different directions so that all 4 sides of the pan are covered. It's okay if you still see the corners.
Preheat the oven to 350°F and place a rack in the center of the oven.
Put the chocolate chips and vegan butter (or regular butter if you are using dairy) in a heat-proof bowl. Place the bowl over a small pot with about 1” of water in it to create a double boiler. Bring the water to a simmer over medium-low heat.
As the steam from the simmering water melts the chocolate and butter, stir them every 30-60 seconds with a rubber spatula to keep them from scorching. Once there are no more unmelted lumps in the bowl, remove it from the heat and set it aside.
In a separate small bowl, combine the flour, cocoa powder, white and brown sugar, baking powder, and salt and stir them until well combined. Add them to the melted chocolate and vegan butter and stir until the mixture just begins to come together.
When the dry ingredients are mostly incorporated, add the milk and vanilla and continue stirring until the brownie batter is smooth. It will be a fairly thick batter.
Spread the brownie batter in the parchment-lined baking dish. Then, bake for 35-40 minutes, or until a knife or toothpick inserted in the center comes out clean or with only a few moist crumbs on it.
Remove the brownies from the oven and allow them to cool. Cut them into 9 squares for large brownies or 16 squares for smaller servings.