In a medium bowl, combine the brown sugar,cinnamon, and butter and mix together with a spoon until blended. Stir in the oatmeal until the mixture is crumbly.
Set this topping aside while preparing the batter.
Heat the oven to 375 F. Grease a 13x9-inch pan with unsalted butter, or solid shortening, or spray with a nonstick cooking spray containing flour, and set aside.
Crack the eggs into a large bowl and beat with a fork or wire whisk until combined. Add the milk and mix well until smooth. Add the sugar, oil, and vanilla and mix until blended.
Sift together the flour, baking powder, baking soda, salt, and nutmeg. Add the dry ingredients to the egg mixture and mix with a spoon for 20 to 30 strokes just until combined and all the dry ingredients are moistened. The batter will be lumpy but that's OK. That's what makes the cake more tender.
Pour the batter into the prepared baking pan.Sprinkle the reserved oatmeal streusel mixture evenly over the batter.
Bake the coffee cake for 25 to 35 minutes until it is puffed and golden brown, and a toothpick inserted in the center comes out clean.Let cool for about 15 minutes, and cut into squares to serve.