For the Apple Coffee Cake with Cinnamon Crumb Topping:

1. Before You Begin: Make sure all ingredients for the cake are at room temperature before starting, including the butter, egg, Greek yogurt (or sour cream), and applesauce. This helps the ingredients incorporate smoothly and creates a more even, tender crumb.
2. Preheat your oven to 325°F. Grease an 8×8-inch square baking pan and line with parchment paper, leaving some overhang for easy removal. 
3. Prepare the cinnamon apples. In a medium bowl, combine the diced apples, brown sugar, and cinnamon. Toss until the apples are evenly coated, then set aside while you prepare the remaining components.
4. Make the cinnamon crumb topping. In a separate bowl, whisk together the flour, brown sugar, granulated sugar, cinnamon, pumpkin pie spice, and salt. Pour in the melted butter and stir with a fork until the mixture forms moist, buttery crumbs. You should have a combination of small and large clumps. Set aside.
5. Now start on your cake base. In a large mixing bowl, beat the softened butter, granulated sugar, and brown sugar together using a hand mixer or stand mixer fitted with the paddle attachment. Beat for approximately 2–3 minutes, until lighter in color and fluffy, scraping down the sides of the bowl as needed.
6. Beat in the egg, Greek yogurt (or sour cream), applesauce, and vanilla, until just combined. Don’t worry if the mixture looks a little separated, it will come together when you add the dry ingredients.
7. Add in the baking powder, salt, and all purpose flour, and mix only until no flour streaks remain. Avoid overmixing.
8. Assemble the coffee cake. Spread the cake batter evenly into your prepared baking pan using an offset spatula or the back of a spoon. Distribute the cinnamon apples evenly over the batter, followed by the cinnamon crumb topping. Gently squeeze some of the crumb mixture together with your fingers as you sprinkle it over the apples to create larger, bakery-style clusters.
9. Transfer to the preheated oven and bake for approximately 65–75 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs. 
10. Allow the coffee cake to cool in the pan for at least 20–30 minutes before removing and slicing. Serve slightly warm or at room temperature.
11. The cake will keep at room temperature loosely covered for 3 days, or wrapped tightly in the fridge for up to a week.