Preheat the over to 425° F and grease an 8x8 square pan or line with parchment paper

In a large bowl, combine the flour, baking soda, sugar, and cocoa and set aside

In a food processor or blender mix the yogurt, soy milk, oil, and vanilla until smooth

Pour the yogurt mixture into the dry ingredients, stirring until well combined

Pour the batter into the greased pan and bake for 25 minutes, or until the brownies spring back when touched

Cool the brownies to room temperature before slicing