Prep Pan and Oven: Coat 9x13-inch baking dish with non-stick cooking spray. Preheat oven to 350 degrees F (177 degrees C).
Prepare Streusel: To a medium bowl, add flour, white sugar, brown sugar, cinnamon, and cloves, then whisk to combine.
Cut in Butter: Add cold cubed butter and cut in with pastry cutter or two forks until mixture forms coarse crumbs. If butter warms and mixture becomes greasy, chill streusel in refrigerator until crumbs firm up.
Chill Streusel: Transfer streusel to fridge while making batter so crumbs stay crumbly and easy to sprinkle. (Don't skip this step. Cold stresuel will ensure the top of the cake is crumbly.)
Cream Butter and Sugar: In large bowl, cream softened butter and sugar with an electric mixer on medium speed until mixture looks lighter and smooth. If butter is too cold and lumps remain, let soften a few minutes and try again.
Add Eggs: Add eggs one at a time, mixing each in before adding next and scraping bowl sides with a rubber spatula as needed. If batter looks curdled after eggs, keep mixing briefly; curdling often resolves when wet ingredients are added.
Add Wet Ingredients: Add sour cream, applesauce, and vanilla extract and mix on low until combined. If sour cream is very cold and causes small lumps, mix a little longer on low to smooth batter.
Whisk Dry Ingredients: In a separate medium bowl, whisk flour, baking powder, cinnamon, baking soda, and salt until evenly distributed.
Combine Wet and Dry Ingredients: Add some flour mixture to butter mixture and stir with wooden spoon until flour is nearly incorporated. Add remaining flour mixture and stir until flour just disappears. If batter seems very stiff after adding flour, fold gently rather than stirring hard; if it still seems dry, fold in a splash of milk or sour cream.
Layer Batter and Streusel: Spread enough batter to cover bottom of prepared pan, smooth top, sprinkle a portion of chilled streusel evenly, add remaining batter in dollops and smooth gently, then top with remaining streusel. Press streusel lightly so it holds but do not compact it.
Bake: Place pan in preheated oven and bake for 35-40 minutes, until toothpick inserted into center comes out clean or with a few moist crumbs. If top browns too quickly or oven has hot spots, rotate pan halfway through baking and tent loosely with foil if needed. Check cake starting near end of baking time since oven heat varies.
Cool Before Serving: Remove cake from oven and cool in pan until just warm before cutting. Cutting too soon while very hot can cause cake to fall apart; if cake seems sticky when slicing, let cool longer.