Combine 2 cups flour, undissolved yeast, sugar and salt in a large bowl. Add warm water, oil and egg and beat for 2 minutes until smooth. Add remaining 2 cups flour and raisins; beat until well mixed. Cover. Let rest 10 minutes.
Stir dough and pour into greased 15 x 10-inch pan with sides. Pat out smoothly with floured hands. Sprinkle brown sugar, sugar and cinnamon over dough. Drizzle milk over the top. Cover loosely and let rise in warm, draft free place until doubled, about 30 to 45 minutes.
Bake at 350°F for 20 to 25 minutes until well browned. Cool slightly on wire rack. Combine frosting ingredients and drizzle over warm coffee cake. Serve warm.