Preheat oven to 350F. Grease a 9-inch round baking pan by spraying it with nonstick spray. Set aside.
In a medium bowl, add all ingredients for the crumb topping.
1/2 cup cold unsalted butter, 3/4 cups all purpose flour, 1/3 cup granulated sugar, 1/3 cup light brown sugar, 1/4 cup old fashioned rolled oats, 1/4 teaspoon kosher salt
Using a pastry cutter or fork, cut the butter into the dry ingredients until it forms a pea-sized crumb.
Place bowl in the fridge to chill until ready to use later.
To make the cake, add butter and sugar to the bowl of your stand mixer, fitted with the paddle attachment. Beat for 4-5 minutes, or until pale, light, and fluffy.
6 tablespoons unsalted butter, 3/4 cup granulated sugar
Add eggs, vanilla, and yogurt. Beat again until well combined.
2 large eggs, 1 teaspoon vanilla extract, 2/3 cup plain Greek yogurt
Add flour, cinnamon, baking powder, baking soda, and salt. Mix until the flour is just incorporated into the batter.
1 ½ cups all purpose flour, 1 teaspoon ground cinnamon, 1 teaspoon baking powder, 1/4 teaspoon baking soda, 1/4 teaspoon kosher salt
Add apples to the bowl. Using a rubber spatula, fold apples into the batter until distributed throughout.
3 cups peeled and diced Granny Smith apples
Pour batter into the prepared baking pan. Use the rubber spatula to make the top even from edge to edge.
Sprinkle crumb topping on top of the batter.
Bake for 65-75 minutes, or until a toothpick inserted in the center comes out clean. If the crumble on top starts to brown too much while cooking, you can tent the top with foil.
Let cool in the pan for 15 minutes, while you prepare the custard topping.
To make the custard sauce, add milk and heavy cream to a medium saucepan over low heat.
1/2 cup whole milk, 1/2 cup heavy cream
Heat until it starts to simmer around the edges of the pot. Do not boil!
Remove from heat.
In a separate bowl, add sugar and egg yolks. Beat with a hand mixer for about 1 minute 30 seconds, or until pale, thick, and creamy.
1/4 cup granulated sugar, 3 large egg yolks
Slowly whisk the heavy cream into the egg yolks to slowly bring up their temperature. This will prevent the eggs from scrambling.
Once all heavy cream has been poured into the yolk mixture, pour it all back into the pot and heat over low heat, while constantly whisking to thicken to coat the back of a spoon. This may take about 6-8 minutes, and it will thicken more as it cools. If the sauce splits, you can use an immersion blender to blend it back together to make it smooth and creamy.
Remove from heat and stir in the vanilla bean paste.
1 teaspoon vanilla bean paste
Serve cake with custard sauce poured over top.
