To prepare batter, place oats in a food processor; process until finely ground (about 1 minute). Lightly spoon flour into a dry measuring cup; level with a knife. Add flour, sugar, baking powder, and salt to food processor; process until well blended. Add butter; pulse 5 times or until combined. Spoon mixture into a large bowl. Combine milk, egg substitute, and vanilla, stirring just until blended. Add to oat mixture, stirring to combine. Gently stir in blackberries. Pour mixture into a 9-inch square baking pan coated with cooking spray (batter will be thin).
To prepare topping, combine 1/2 cup oats and remaining ingredients in a food processor; process until finely chopped. Sprinkle evenly over batter. Bake at 350° for 45 minutes or until lightly browned and a wooden pick inserted in the center comes out clean. Cool completely on a wire rack.