Preheat your oven to 350°F and grease a 9x13 inch baking dish (or 8x8 if you prefer thicker brownies). While the oven preheats, combine the vegan cream cheese, 1/3 cup sugar, cornstarch, lemon juice, 2 tsp vanilla, 1/4 tsp salt, and nutritional yeast in a bowl. Mix until completely smooth and creamy—this filling should be thick but pourable. Set aside. I like to use freshly squeezed lemon juice here because it gives the cheesecake filling a brighter, more authentic tang that really cuts through the richness.

In a separate bowl, combine the vegan butter with 1 1/2 cup sugar and mix until well blended. Add the room-temperature non-dairy milk and 3 tsp vanilla, stirring until the mixture is smooth and emulsified. In a third bowl, whisk together the flour, cocoa powder, 3/4 tsp baking powder, 1/4 tsp salt, and espresso powder. Fold the dry ingredients from Step 2 into the wet mixture, stirring gently until just combined—don't overmix, as this keeps the brownies tender. Room-temperature milk really does help the batter come together smoothly, so don't skip that detail if you can help it.

Pour most of the brownie batter (reserving about 1/4 cup) into your prepared baking dish, spreading it into an even layer. Pour the cheesecake filling from Step 1 over the brownie batter, spreading it gently to cover. Thin the reserved 1/4 cup brownie batter with 1-2 tablespoons of water until it's drizzle-able. Using a fork or knife, create swirls by dragging the thinned brownie batter across the cheesecake surface in decorative lines. The swirls not only look beautiful but also create pockets of intense chocolate flavor throughout.

Bake in your preheated 350°F oven for 30-35 minutes, until the cheesecake layer is set but still has a slight jiggle in the center and the brownie edges are firm. Remove from the oven and allow to cool completely at room temperature for at least 2 hours before cutting—this cooling time is essential for the layers to set properly and make clean slices.