Measure out 1 cup of ice cream and set aside to soften on counter while moving on to the next step.
Cut butter into 8-10 small pieces. In a large bowl, use a pastry blender to mix butter into the flour until the mixture resembles coarse crumbs (much like you would do while making pie crust).
Add ice cream in the same way, cutting into the flour mixture until a dough forms. You can use a stand mixer with a dough hook for this step if you have one.
Knead dough 6-8 strokes or until smooth. Cut into 3 separate discs. Wrap discs in plastic wrap and refrigerate overnight (up to 3 days).
When ready to bake, preheat oven to 400°F. Roll out dough to ¼ inch thickness between a floured surface on bottom and the plastic wrap on top to keep dough from sticking to the rolling pin. Use a circle cutter to cut out cookies. Each disc should yield 1 dozen cookies.
Place parchment paper or a silicone baking mat on top of your baking sheet. This will make any fruit preserve spills easy to clean up. Transfer cookies to the baking sheet. Using your thumb, make an indent into each cookie and fill with ½ teaspoon fruit preserves or cream cheese filling.
Bake for 12 minutes. Cool 5 minutes and transfer to wire rack to cool completely. Dust with powdered sugar before serving.