Preheat the oven to 350 degrees Fahrenheit. Line an 8x8 inch baking dish with parchment paper if desired.
In a medium bowl, whisk together the sugars, vegan milk, vegan butter, applesauce, and vanilla until smooth. Add the flour, cocoa powder, and salt and mix until just combined. Fold in the chocolate chunks.
Spread the batter into the prepared baking dish. Add dollops of the pistachio spread in several different spots, then use a butter knife to swirl the spread throughout the batter.
Bake in the preheated oven for 35-45 minutes, until a toothpick inserted into the center away from the pistachio spread comes out clean.
Sprinkle with flaky sea salt, then let cool to room temperature before slicing and serving!