Preheat the oven to 350°F (175°C). Line a standard 12-cup muffin pan with cupcake liners.
Whisk the flour, baking powder, and salt together in a medium bowl.
Beat ½ cup butter with ¾ cup sugar for 2–3 minutes, until pale and fluffy.
Beat in the eggs one at a time. Add 2 teaspoons vanilla and the milk.
Fold the dry ingredients into the wet mixture in two portions. Stop when no dry flour remains.
Beat 8 oz cream cheese until smooth. Add ¼ cup sugar, egg yolk, and ½ teaspoon vanilla. Mix until creamy.
Add about 1½ tablespoons cupcake batter to each liner.
Place about 1 tablespoon cheesecake filling in the center of each. Cover with remaining cupcake batter until the liners are about ¾ full.
Bake for 18–22 minutes, until the cake portion is set and a toothpick inserted near the edge comes out with a few moist crumbs.
Cool in the pan for 5 minutes, then transfer to a wire rack and cool completely.
Cook the strawberries, ¼ cup sugar, and lemon juice over medium-low heat for 6–8 minutes. Mix cornstarch with water, stir it in, and cook for another 1–2 minutes. Cool completely.
Beat 4 oz cream cheese and ¼ cup butter for 1–2 minutes. Gradually mix in powdered sugar and 1 teaspoon vanilla until smooth.
Pipe or spoon the cream cheese frosting onto the cooled cupcakes.
Top each cupcake with 1–2 teaspoons of cooled strawberry topping.
Refrigerate for at least 30 minutes before serving.
