Preheat oven to 350°.
Combine first 3 ingredients in a small bowl; let stand 10 minutes. Stir in egg substitute and vanilla.
Pour butter in the bottom of a 9-inch cake pan coated with cooking spray. Sprinkle with 1/4 cup sugar. Arrange the apple slices spokelike on top of sugar, working from center of pan to edge.
Lightly spoon flour into dry measuring cups; level with a knife. Combine 3/4 cup sugar, flour, baking soda, cinnamon, salt, and nutmeg in a large bowl; stir with a whisk. Add oat mixture; stir just until moist. Pour batter into prepared pan.
Bake at 350° for 40 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 10 minutes. Place a plate upside down on top of cake; invert onto plate. Cut into wedges.