Prepare the Dry Ingredients : In a medium-sized mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
Cream the Butter and Sugars : In a large bowl, use a hand or stand mixer to beat the softened butter, brown sugar, and granulated sugar together until light and fluffy (about 2–3 minutes).
Add the Wet Ingredients : Mix in the cold egg, vanilla extract, and almond extract until fully combined. The mixture may look slightly curdled, but that's normal.
Combine Wet and Dry Ingredients : Gradually add the dry ingredients to the wet ingredients and mix on low speed until just combined. Do not overmix.
Fold in the Mix-ins : Gently fold in the freeze-dried raspberries and white chocolate chips, being careful not to crush the raspberries too much. Chill the dough in the refrigerator for at least 30 minutes to allow the flavors to develop and prevent spreading during baking.
Shape the Cookies : Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper. Scoop about 1.5 tablespoons of dough for each cookie and place it on the baking sheet, leaving about 2 inches of space between each cookie. Using a small spoon, create a shallow well in the center of each cookie and fill it with a small dollop of raspberry jam.
Bake : Bake the cookies for 10–12 minutes or until the edges are lightly golden but the centers still look slightly underbaked. Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.