Preheat your oven to 350°F and line a small 8x8-inch baking dish with parchment paper, leaving slight overhang on two sides for easy removal. Meanwhile, cut the vegan butter into a few chunks and place in a small saucepan over medium-low heat. Watch carefully as it melts and the milk solids brown—you'll see golden-brown flecks at the bottom after about 5-7 minutes. This browning step is crucial for developing that rich, nutty depth of flavor that defines these brownies.

Remove the browned butter from heat and immediately pour it over the chopped vegan chocolate in a bowl. Let it sit undisturbed for 2 minutes to allow the residual heat to melt the chocolate completely. Stir until smooth and silky, then add the cocoa powder and instant espresso powder, whisking until fully incorporated. I like to add the espresso powder here because it intensifies the chocolate flavor without adding bitterness—it's a secret weapon for depth.

In a separate bowl, combine the room-temperature milk, both sugars, yogurt, vanilla, and salt. Whisk vigorously for about 1-2 minutes until the sugars begin to dissolve and the mixture becomes slightly pale and fluffy. This aeration helps create a tender crumb and ensures even sugar distribution throughout the brownies.

Pour the wet ingredient mixture from Step 3 into the chocolate mixture from Step 2, stirring gently but thoroughly until fully combined and no streaks remain. The batter should be smooth and glossy at this point.

Sift the flour over the batter and fold it in gently with a spatula using a few strokes as possible—overmixing develops gluten and creates tough brownies. Once the flour is almost completely incorporated, add the chocolate chips and fold just until combined. I always use King Arthur all-purpose flour because it has the right protein content for these brownies, but any quality all-purpose flour works well.

Pour the batter into your prepared 8x8-inch baking dish, smoothing the top gently with a spatula. Bake for 33-35 minutes until a toothpick inserted in the center comes out with a few moist crumbs attached (not completely clean, as you want them fudgy). The edges should look set but the center should still jiggle slightly when you gently shake the pan.

Remove the brownies from the oven and let them cool in the pan for 20-30 minutes. This cooling time allows the crumb structure to set properly so they hold together cleanly when you cut them. Once cooled, use the parchment overhang to lift the entire slab out of the pan, then cut into squares with a sharp knife (wiping the blade between cuts prevents sticking).