Preheat the oven to 375°F/190°C. Line a 12-cup muffin pan with paper liners.
Peel, core, and dice the apples into approximately ¼-inch pieces. Toss with 1 tablespoon of the orange juice, then add the cornstarch and toss until evenly coated.
Melt 1 tablespoon butter in a small saucepan over medium heat. Add the remaining tablespoon of orange juice, sugar, cinnamon, and salt. Add the apples and cook for 3 to 5 minutes, stirring regularly, until they begin to soften and the juices have thickened enough to cling to the fruit. If the mixture becomes too thick before the apples soften, add a small splash of orange juice. Remove from the heat and set aside to cool.
To make the muffin batter, beat the softened butter, 2 ounces cream cheese, sugar, and egg until pale and well blended. Mix in the milk.
Add the flour, baking powder, and salt and mix just until combined. Don't overmix.
To make the cheesecake filling, beat the 4 ounces cream cheese, sugar, egg yolk, and vanilla together until smooth.
Divide enough muffin batter among the prepared cups to fill each approximately one-quarter full.
Spoon a rounded tablespoon of cheesecake filling into the center of each, followed by approximately 1 tablespoon of the apple mixture.
Divide the remaining muffin batter over the filling. There's no need to spread it perfectly.
Make the topping by combining the melted butter, sugar, flour, and cinnamon until moist crumbs form. Divide evenly over the muffins.
Bake for 20 to 25 minutes, or until the muffins are risen and golden.
Cool in the pan for 5 minutes, then transfer to a wire rack and allow to cool completely.
Notes
Erren’s Top Tips
Keep the apples small. A small dice means you get apple throughout the center without large pieces breaking up the muffin.Don't overcook the apples. Three to five minutes is enough to give them a head start. They'll continue cooking inside the muffins.Watch the consistency rather than the clock. The apple mixture should be thick with no loose juice pooling in the pan. If it becomes overly thick before the apples soften, add a small splash of orange juice.Don't thin the muffin batter. It's supposed to be thicker than an everyday muffin batter. That thickness helps keep the cheesecake and apple filling suspended in the center.Don't overmix once the flour goes in. Mix only until you no longer see dry streaks of flour.Let them cool. The cheesecake center continues to set as the muffins cool, so resist cutting into one straight from the oven.
Variations & Add-Ins
Apple Pie Spice: Replace the cinnamon in the apple mixture with apple pie spice for extra warmth.Add Nuts: Chopped pecans or walnuts can be added to the crumb topping for crunch.Caramel Apple: Drizzle completely cooled muffins with a little caramel sauce just before serving.Pear Cheesecake Muffins: Firm pears can replace the apples for a softer, more delicate fruit filling.
Storage & Freezing
Because these muffins contain a cheesecake filling, I recommend storing them covered in the refrigerator once completely cooled. They'll keep well for about 3 to 4 days.For the best texture, let a refrigerated muffin sit at room temperature for 15 to 20 minutes before eating.To freeze, cool the muffins completely and wrap them individually before placing them in an airtight freezer container or freezer bag. Freeze for up to 2 months. Thaw overnight in the refrigerator.