Prepare the oven and pan. Preheat the oven to 350°F. Line an 8×8-inch baking pan with parchment paper, leaving enough overhang on the sides to lift out the brownies later.
Combine the wet ingredients. Add the melted vegan butter and granulated sugar to a mixing bowl and whisk to combine. Add the non-dairy milk and vanilla extract and whisk again until evenly mixed.
Mix the dry ingredients. In a separate bowl, whisk together the flour, cocoa powder, espresso powder, baking powder, and salt. Break up any visible lumps of cocoa.
Make the batter. Add the dry ingredients to the wet mixture. Stir with a spatula just until no dry streaks of flour or cocoa remain. Avoid continuing to mix once the batter comes together.
Add the chocolate. Fold in the vegan chocolate chips until evenly distributed throughout the thick batter.
Fill the pan. Transfer the batter to the prepared baking pan. Spread it evenly into the corners and smooth the top with a spatula.
Bake. Bake for 25–30 minutes. The edges should look set and the center should no longer appear like raw batter. A toothpick inserted near the center should come out with moist crumbs rather than completely clean.
Cool. Let the brownies cool in the pan for about 30 minutes. Lift them out using the parchment paper, transfer to a wire rack, and cool completely before cutting into 16 squares.
