Process the cookies, sugar, butter, flour and cinnamon in a food processor just until crumbly, about 5 minutes. Set aside.
Preheat oven to 350 °F.
Grease the muffin tins or use appropriate paper liners.
Sift together the flour and baking powder.
Cream the sugar, butter, salt in with an electric mixer on medium speed with the paddle, scraping down the bowl periodically, until the mixture is smooth and light in color, about 5 minutes.
Whisk together the eggs, milk, vanilla and oil. Add to the butter-sugar mixture in two or three additions, mixing until fully incorporated after each addition and scraping down the bowl as needed.
Add the sifted dry ingredients, diced apples and mix on low speed until evenly moistened.
Pour about 3 oz of batter into each prepared muffin cup, filling them three-quarters full. Gently tap the filled tins to release any air bubbles. Sprinkle with crumble.
Bake at 375 °F until a toothpick inserted near the center of a muffin comes out clean, about 30 minutes.
Cool the muffins in the tins for a few minutes, then unmold and transfer them to wire racks to cool completely.