1. Make the Custard Sauce (Ahead of Time):

• Heat Milk: Gently bring the milk (or cream/half-and-half) just to a simmer in a medium saucepan over medium heat. Do not boil.
• Mix Yolks & Sugar: Meanwhile, in a medium bowl, whisk the egg yolks and sugar together until well combined and slightly pale.
• Temper Eggs: Once the milk is simmering, remove it from the heat. Slowly drizzle about half a cup of the hot milk into the egg yolk mixture while whisking constantly. This gently warms the yolks (tempering) to prevent scrambling.
• Combine and Cook: Pour the tempered egg yolk mixture back into the saucepan with the remaining hot milk. Return the saucepan to medium-low heat.
• Cook Gently: Cook, stirring constantly with a silicone spoon or spatula (scraping the bottom and sides), until the mixture thickens enough to coat the back of the spoon (Nappé consistency). If you draw a line through the coating on the spoon, it should hold its shape. This happens slowly; do not rush or increase heat too much, or it will curdle. The final consistency will be like thin cream, not thick pudding; it thickens upon cooling.
• Strain and Flavor: Immediately remove from heat. Pour the custard through a fine-mesh sieve into a heatproof jar or bowl to catch any potential lumps. Stir in the vanilla extract.
• Chill: Press a piece of plastic wrap directly onto the surface of the custard to prevent a skin from forming. Refrigerate until completely chilled (at least 2-3 hours, or preferably overnight).  

2. Make the Streusel Topping:

• In a medium bowl, combine the flour, sugar, and rolled oats.
• Add the small pieces of cold butter.
• Using a pastry blender, a fork, or your fingertips, cut or rub the butter into the dry ingredients until the butter is incorporated and the mixture has a coarse, crumbly texture.
• Place the streusel mixture in the refrigerator to keep cold until ready to use.

3. Prepare Oven and Pan:

• Preheat the oven to 350°F (175°C).  
• Grease a 9-inch springform pan well.

4. Make the Cake Batter:

• In a large bowl using an electric mixer, cream together the room temperature butter and 1/2 cup granulated sugar until light and fluffy.
• Beat in the room temperature eggs, one at a time, mixing well after each addition.
• In a separate small bowl, whisk together the 1 1/4 cups all-purpose flour, baking powder, cinnamon, and salt.
• Gradually fold the dry ingredients into the butter/sugar mixture alternately with the milk or cream (start and end with dry). Mix gently until just combined. Do not overmix.

5. Assemble the Cake:

• Spoon the cake batter into the prepared springform pan and smooth it out evenly.
• Arrange the thinly sliced apples over the top of the batter in an even layer (no need for a perfect pattern).
• Sprinkle the chilled streusel topping evenly over the apples.

6. Bake the Cake:

• Bake for about 50 minutes to 1 hour, until the top is lightly browned, the streusel is crisp, and a toothpick inserted into the center of the cake (not just apples) comes out clean or with only moist crumbs attached.
• Let the cake cool in the pan on a wire rack for about 15-20 minutes.

7. Serve:

• Carefully release and remove the sides of the springform pan.
• Dust the cooled (or slightly warm) cake with confectioner’s sugar just before serving.
• Serve slices warm or at room temperature with the chilled custard sauce poured alongside or over the top.