Make the cheesecake filling. Beat the cream cheese, sugar, vanilla, and a pinch of salt until smooth and fluffy. Scoop 12 small mounds (about 1 tablespoon each) onto a parchment-lined plate. Freeze for at least 45 minutes, or until firm.

Cook the apples. In a small skillet over medium heat, melt butter. Add diced apples, brown sugar, cinnamon, lemon juice, and a pinch of salt. Cook 4–6 minutes, stirring, until the apples are tender and most liquid has evaporated. Spread on a plate to cool completely.

Whisk dry ingredients. In a bowl, combine flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Set aside.

Cream butter and sugars. In a large bowl, beat butter with granulated and brown sugar until light and fluffy, about 2–3 minutes. Add the egg, egg yolk, and vanilla. Mix until smooth.

Bring the dough together. Add the dry ingredients to the wet in two additions. Mix just until no streaks remain. Fold in the cooled apples gently. Chill the dough for 30 minutes to make it easier to handle.

Preheat and prep. Heat oven to 350°F (175°C). Line two baking sheets with parchment paper.

Assemble the cookies. Scoop 24 portions of dough (about 1 1/2 tablespoons each). Flatten one piece into a small disk. Place a frozen cheesecake mound in the center. Top with another dough disk and pinch edges to seal, rolling gently into a ball. If using, roll in cinnamon sugar. Repeat with remaining dough and filling.

Bake. Arrange cookies 2 inches apart. Bake 11–13 minutes, until edges are set and lightly golden but centers still look soft. Do not overbake; they’ll firm up as they cool.

Cool. Let cookies rest on the sheet for 10 minutes, then transfer to a rack. They’re best slightly warm when the center is creamy, or chilled if you prefer a cheesecake-like bite.