Preheat your oven to 350°F (175°C). In a large bowl, cream the butter and sugar until light and fluffy. Add the egg and vanilla extract, mixing until combined. In another bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, mixing until a dough forms.

In a small saucepan, combine raspberries, sugar, and cornstarch. Cook over medium heat, stirring frequently, until the mixture thickens and the raspberries break down, about 5-7 minutes. Remove from heat and let cool slightly.

Roll the cookie dough into 1-inch balls and place on a lined baking sheet. Use your thumb to create an indentation in each ball. Spoon a small amount of raspberry filling into each indentation. Sprinkle reserved dough crumbs over the filled cookies.

Bake in the preheated oven for 12-15 minutes, until edges are lightly golden. Let the cookies cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.

Serve the cookies warm or at room temperature. They pair wonderfully with milk, tea, or coffee. For an extra treat, add a dollop of whipped cream or a scoop of ice cream on the side.

Store the cookies in an airtight container at room temperature for up to 5 days. For longer storage, place them in the refrigerator for up to a week. Reheat in the oven if desired.