Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, brown sugar, granulated sugar, baking powder, and salt until well combined.
In a large bowl, cream the softened butter with an electric mixer until light and fluffy, about 2-3 minutes.
Add the egg and vanilla extract to the butter mixture, mixing until fully incorporated.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Scoop about 1 tablespoon of dough and flatten it slightly in your hands. Place a small spoonful of fruit preserves in the center, then fold the dough over to encase the filling. Pinch the edges to seal.
Place the filled cookies on the prepared baking sheet, spacing them about 2 inches apart.
Bake for 12-15 minutes, or until the edges are lightly golden.
While the cookies are baking, prepare the icing by mixing the powdered sugar with 1-2 teaspoons of milk until smooth. Adjust the consistency as needed.
Once the cookies are out of the oven and cooled slightly, drizzle the icing over the top and add sprinkles if desired.