Make the apple filling. In a skillet over medium heat, melt butter. Add diced apples, brown sugar, granulated sugar, cinnamon, nutmeg, lemon juice, and salt. Cook, stirring, until the apples soften, about 5–6 minutes.

Thicken it. Stir in the cornstarch slurry and cook 1–2 more minutes, until glossy and slightly jammy. Transfer to a plate and cool completely. For faster cooling, spread it out and chill briefly in the fridge. The filling should be thick, not runny.

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

Cream the butter and sugars. In a large bowl, beat softened butter with granulated and brown sugars until light and fluffy, 2–3 minutes. Add egg and vanilla; beat until smooth. Mix in milk.

Combine. Add dry ingredients to wet and mix on low until just combined. Don’t overmix. The dough should be soft but not sticky. If it feels too sticky, chill 15–20 minutes.

Prep to assemble. Heat oven to 350°F (175°C). Line two baking sheets with parchment. Stir the rolling sugar and cinnamon together in a small bowl.

Portion the dough. Scoop about 2 tablespoons of dough per cookie. Flatten each portion into a 3-inch disk in your palm or on a lightly floured surface.

Add the filling. Place about 1 to 1 1/2 teaspoons of cooled apple filling in the center. Don’t overfill. Gently fold the edges of the dough up and over the filling, pinching to seal well. Roll into a smooth ball with the seam side down.

Coat and arrange. Roll each ball in the cinnamon sugar, then set on the baking sheet, spacing 2 inches apart. Lightly flatten the tops with your fingertips for an even bake.

Bake. Bake 10–12 minutes, until the edges are set and the tops look just dry with faint cracks. The centers should still look soft—don’t overbake.

Cool. Let cookies rest on the sheet 5 minutes, then move to a rack to cool. If using, drizzle with caramel and a pinch of flaky salt once just warm.