Prepare the apple filling: In a small saucepan, combine the diced apples, 1/4 cup of granulated sugar, 1 teaspoon of cinnamon, nutmeg, and lemon juice. Cook over medium heat for 5–7 minutes until the apples are soft. Remove from heat and let cool completely.
Make the cookie dough: In a large bowl, cream the softened butter and 1 1/2 cups of granulated sugar until it’s light and fluffy. Then, add the eggs and vanilla extract, mixing until smooth.
Mix the dry ingredients: In a separate bowl, whisk together the flour, baking soda, cream of tartar, and salt. Gradually add this dry mixture to the wet mixture, stirring until everything is combined.
Assemble the cookies: Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper. Scoop out 1 tablespoon of dough, flatten it in your palm, and add a small spoonful of the cool apple filling in the center. Cover with another piece of dough, seal the edges, and roll into a ball.
Coat and bake: Roll each ball in a mix of 1/4 cup granulated sugar and 1 teaspoon cinnamon, and place them 2 inches apart on the baking sheet. Bake for 10–12 minutes, or until the edges are golden brown. Cool them on a wire rack and serve warm or at room temperature.