Preheat your oven to 350°F (175°C).
Grease and line an 8x8-inch baking pan with parchment paper.
In a saucepan, melt the dairy-free butter over low heat. Remove from heat and stir in the chocolate until melted and smooth.
In a large bowl, whisk together the flour, granulated sugar, light brown sugar, dark cocoa powder, and salt.
In another bowl, mix the melted chocolate mixture, dairy-free milk, applesauce, and vanilla extract.
Add the wet ingredients to the dry ingredients and stir until just combined.