Preheat oven to 350°F and grease a 8x8 square inch pan.
Start by making the streusel topping to allow the butter enough time to cool. Melt the butter in the microwave, and set aside while you combine the rest of the streusel ingredients in a separate bowl (flour, brown sugar, cinnamon and salt). Then, pour the cooled butter on top of the dry ingredients. Stir until combined. You should see small pea-sized balls starting to form. Set aside. This is your streusel topping.
In a small bowl, combine 1/3 cup of brown sugar and 1 tsp of cinnamon. Set aside. This is your cinnamon and brown sugar layer.
In another small bowl combine the oil, egg, vanilla, and milk together. Stir until thoroughly mixed. This is part 1 of your cake mixture.
In a large bowl, combine the rest of coffee cake ingredients (flour, granulated sugar, baking powder, and salt). This is part 2 of your cake mixture.
Pour the egg & oil mixture (from Step 4) into the dry ingredients bowl (from Step 5). Mix together well. This is your final cake batter mixture.
Spread half of the cake batter mixture onto the bottom of your prepared pan. The batter will be very thick, but still spreadable. Spread it out as evenly as possible with a spoon so that it nearly covers the bottom of the pan. It's okay that it's a very thin layer of batter or if it doesn't cover the bottom totally, as it will get filled in later with the rest of the batter.
Sprinkle the brown sugar and cinnamon mixture (that you prepared in Step 3) over the first layer of the cake batter in the pan. Note: You can skip this step for a lighter version of this recipe.
Pour the rest of the batter on top of the brown sugar layer, and spread it out evenly. Sprinkle the streusel layer evenly on top of the second cake batter layer.
Bake for 18 to 20 minutes or until a toothpick comes out clean. Let cool.
Once the cake is completely cool, combine the powdered sugar, vanilla, and the milk until a thick glaze forms. Drizzle the glaze over the cooled coffee cake and serve.