Topping: combine whole wheat flour, brown sugar, cinnamon, nutmeg, and oil in a small bowl and mix together, then set aside.
Batter: Sift whole wheat flour, baking powder, and salt and set aside. In a separate bowl, beat egg until frothy. Beat in sugar and oil until combined. Add milk, sour cream, and vanilla. Slowly add flour mixture, mix on low until combined.
Put 1/2 the batter in a 9x9 - inch greased pan and spread evenly. Sprinkle 1/2 of the topping over batter. Repeat. Bake at 350 degrees in a preheated oven for 25 to 30 minutes.