Put the diced apples in a medium saucepan with both sugars, the cinnamon, nutmeg, cornstarch, and lemon juice.

Cook over medium-low heat, stirring gently, for about 5–8 minutes, until the apples soften and the mixture thickens. Turn off the heat and let it cool.

In a large bowl, beat the softened butter, brown sugar, white sugar, and vanilla for 1–2 minutes, until light and fluffy.

Add the egg and beat until fully combined.

In a separate bowl, mix the flour, baking soda, and salt. Add the dry ingredients to the butter mixture gradually and fold until the dough is uniform.

Shape the dough into balls of about 45 g each (a cookie scoop helps). If you like, roll them in sugar.

Use the back of a spoon or your fingers to press a deep well into the center of each ball. Fill with the cooled apple filling.

Arrange on a parchment-lined baking sheet, spaced apart. The cookies spread as they bake.

Bake in an oven preheated to 350°F (175°C) for about 12–16 minutes, until lightly golden.

While they're still hot from the oven, you can shape them into perfect circles with a round cookie cutter. Let them cool completely on the baking sheet before serving.