Grease a glass 10x 15-inch baking dish or a DEEP 9×13-inch baking dish. Set aside.
Cake
In a mixing bowl, beat together the butter and cream cheese until creamy (about 2 to 3 minutes).
Add the brown sugar and white sugar. Beat until fluffy (about 2 to 3 minutes).
Beat in both eggs until combined.
Beat in the vanilla extract until combined.
In a separate bowl, stir together flour, baking soda, baking powder, cornstarch, and salt.
Slowly beat a third of the dry mixture into the wet, then add in half the buttermilk. Beat in another third of the dry mixture and the rest of the buttermilk. Beat the remaining dry mix into the wet. Beat just until combined, but do not over-mix.
Pour half the batter into the prepared baking dish. The batter will be thick.
Lemon Filling
Spread the lemon filling carefully over the batter in the baking dish. Leave about ¾-inch space between the lemon filling and the edge of the pan. Lemon filling that spreads to the outside of the pan will burn while baking. Carefully top with the remaining batter, working from the outer perimeter in to make sure that the lemon filling stays contained within the batter layers.
Cream Cheese Filling
In a medium mixing bowl or the bowl of a standing mixer, beat together the cream cheese filling ingredients: cream cheese, sugar, egg, lemon zest, and lemon juice. Spread the cream cheese layer over the top layer of batter.
Crumble Topping
Whisk together flour, brown sugar, sugar, and cinnamon until well combined. Stir in melted butter with a fork until it is a crumbly mixture and there is no more visible white flour. Sprinkle over the top of the cake.
Bake cake for 60 to 75 minutes or until the center is set and no longer jiggles. Cover the coffee cake with aluminum foil after the first 20 to 30 minutes of baking to prevent the top from burning while the layers underneath cook through. Let the cake cool before adding glaze.
Glaze
Stir together powdered sugar and milk. Drizzle over top of completely cooled cake.
Notes
Lemon pie filling has a great consistency for holding itself in a nice central layer. Lemon curd will also work, especially if it is a thicker lemon curd. Our recipe for homemade lemon curd is more creamy and, though it tastes great, it soaks into the coffee cake more than a premade lemon pie filling.
Using either a 15×10-inch baking dish or a DEEP DISH 9×13-inch will prevent the coffee cake from spilling over the edges.
Keeping the lemon filling to the center and away from the edges of the pan is really important. The coffee cake cooks for so long that if the lemon filling seeps out and is along the edge, it really burns and turns the whole crust to a charred mess.
This is a nice thick, moist cake. It takes quite a while to cook all the layers through completely. Be sure to cover the top with aluminum foil to prevent the crumb topping from burning. You can also place the baking dish on a sheet pan in the oven to catch any spills and reduce browning on the bottom of the coffee cake.