Preheat oven to 350ºF. Line a mini-cupcake pan with mini-cupcake liners, and place a mini Oreo in the bottom of each liner. Set aside.

In a large bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

In a large microwave safe bowl, melt the butter in the microwave and allow to cool a bit. Whisk in the sugar, egg, yogurt, milk, and vanilla extract until combined. Slowly add the wet ingredients to the dry ingredients and stir with a spatula until no lumps remain. Gently stir in crushed Oreos.

Fill the cupcake liners almost to the top with batter. Tap the pan on the counter a few times so the batter can settle around the mini Oreo. Bake for 10-11 minutes or until a toothpick inserted in the center comes out clean. Allow to cool completely before frosting.

In a large bowl with a handheld mixer, or a stand mixer fitted with the paddle attachment, beat the butter on medium speed until creamy, about 2 minutes.

With the mixer on low, add in the powdered sugar, vanilla, and milk or cream. Increase mixer speed to medium and beat until completely smooth, about 3 minutes. If frosting is too stiff, add more milk. If it is too thin, add more powdered sugar. Add salt to taste. If you would like to add crushed Oreos to the frosting, start with 1/2 cup and add more if necessary. Fold the crushed Oreos in with a spatula.

Frost the cupcakes using a piping bag or a large zip top bag with the corner snipped off. Top with crushed Oreos, stick a whole mini Oreo in the top of the swirl, or leave them plain. Cupcakes will stay fresh covered at room temperature up to 3 days.