Preheat the oven to 350°F (175°C) and line the muffin tin with 12 paper cupcake liners.
In a medium bowl whisk together the flour, baking powder, baking soda, and salt and set aside.
In a large bowl beat the softened butter, granulated sugar, and brown sugar with an electric mixer on medium speed until light and fluffy, about 2–3 minutes.
Beat in the eggs one at a time, then mix in the vanilla extract until fully combined.
Add the cookie butter to the wet mixture and beat until smooth and well incorporated.
Add half of the dry ingredients to the wet mixture and mix on low speed just until combined.
Pour in the milk and mix on low speed until just incorporated.
Add the remaining dry ingredients and mix on low speed until a smooth batter forms, scraping the bowl with a spatula as needed.
Divide the batter evenly among the 12 cupcake liners, filling each about two-thirds full.
Bake the cupcakes for 16–18 minutes or until a toothpick inserted in the center comes out clean or with a few moist crumbs.
Transfer the pan to a wire rack and let the cupcakes cool in the pan for 5 minutes.
Remove the cupcakes from the pan and let them cool completely on the wire rack, about 25 minutes.
While the cupcakes cool, make the filling by stirring together the cookie butter and heavy cream in a small bowl until smooth and slightly pourable.
For the frosting, beat the softened butter and cookie butter together in a large bowl until creamy and well blended, about 2 minutes.
Gradually add the powdered sugar on low speed, mixing until thick and smooth.
Add the vanilla extract, salt, and 2 tablespoons of heavy cream or milk, then beat on medium-high speed for 2–3 minutes until fluffy, adding more cream a teaspoon at a time if needed to reach piping consistency.
If using filling, use a small knife or cupcake corer to remove a small cone from the center of each cooled cupcake.
Spoon or pipe about 1 teaspoon of the cookie butter filling into each cupcake cavity, then gently replace a small piece of cake on top to cover the filling.
Fit a piping bag with a large round or star tip and fill it with the cookie butter frosting.
Pipe a generous swirl of frosting onto each cupcake, starting from the outside edge and working toward the center.
Sprinkle the tops with crushed speculoos cookies and press a small cookie piece into each cupcake for decoration.