Preheat oven to 350°F and grease a 9-inch springform pan. Set aside.
Make the custard sauce first: Bring milk to a gentle simmer in a medium saucepan over medium heat. In a separate bowl, whisk egg yolks and sugar until pale yellow, about 2-3 minutes.
Temper the egg mixture: Slowly drizzle about 1/2 cup of hot milk into the egg yolks while whisking constantly. Add another 1/2 cup, then pour the entire mixture back into the saucepan with remaining milk.
Cook the custard: Stir constantly with a silicone spatula over medium heat until the mixture thickens enough to coat the back of a spoon, about 4 minutes. Do not let it boil.
Strain and chill: Pour custard through a fine-mesh sieve into a heatproof bowl. Press plastic wrap directly onto the surface to prevent a skin from forming. Refrigerate until completely chilled.
Prepare streusel topping: In a bowl, work cold butter into flour, oats, and sugar using your fingers or a pastry cutter until mixture resembles coarse crumbs. Refrigerate while preparing cake.
Make the cake batter: Cream room-temperature butter and sugar until light and fluffy, about 3 minutes. Beat in eggs one at a time, mixing well after each addition.
Combine dry ingredients: In a separate bowl, whisk together flour, baking powder, cinnamon, and salt.
Fold in dry ingredients: Add flour mixture to butter mixture alternately with milk, folding gently until just combined. The batter will be thick and sticky.
Prepare the apples: Toss sliced apples with lemon juice and 1 tablespoon flour to prevent sinking during baking.
Assemble the cake: Spread batter evenly in prepared pan. Arrange apple slices in overlapping layers over the batter. Sprinkle chilled streusel topping generously over apples.
Bake: Place in center rack and bake for 50-60 minutes until golden brown and a toothpick inserted in center comes out clean.
Cool and serve: Let cool in pan for 15 minutes before removing springform ring. Dust with confectioners' sugar and serve warm with chilled custard sauce.