Prepare the apple filling by mixing diced apples, flour, sugar, cinnamon, nutmeg, and lemon juice. Set aside.
Make the crumb topping by combining flour, brown sugar, and cinnamon. Cut in cold butter until crumbly. Chill.
Cream butter, granulated sugar, and brown sugar until light and fluffy.
Add egg and vanilla extract, mixing well.
In another bowl, whisk flour, baking soda, cinnamon, nutmeg, and salt.
Gradually mix dry ingredients into wet ingredients until just combined.
Preheat oven to 375°F (190°C) and line baking sheets.
Scoop dough onto baking sheets. Create an indentation in each cookie.
Fill with apple mixture and top with crumb topping.
Bake Apple Crumb Cookies for 15–18 minutes until golden.
Cool slightly before transferring to a wire rack.