Place the refrigerated sugar cookie dough in a large bowl. Add crushed freeze-dried strawberries and flour, and mix until evenly combined. Cover and refrigerate 30-45 minutes.
In a medium bowl, beat cream cheese, powdered sugar, sour cream, vanilla, almond extract, salt, cornstarch, and egg yolk until completely smooth, about 1 minute. Refrigerate until ready to use.
If needed, microwave preserves 10-15 seconds and stir until easily spoonable.
Preheat oven to 350°F. Line two baking sheets with parchment.
Scoop about 2 1/2 tablespoons dough per cookie, spacing 3 inches apart. Press a shallow well in the center of each mound with the back of a spoon.
Spoon 1 1/2 teaspoons cheesecake filling into each well, then top with 1/2 teaspoon preserves. Using a toothpick, swirl the filling and preserves together once or twice. Do not overmix.
Bake 13-15 minutes, until edges are lightly golden and centers are set but soft. Do not overbake.
Cool on the baking sheet 10 minutes, then transfer to a wire rack to cool completely. If desired, garnish with crushed freeze-dried strawberries and a dusting of powdered sugar.
