In a medium bowl, stir together the flour, baking powder and salt.
In a standing mixer, beat together the butter, 1/2 cup sugar, and vanilla extract. Beat for 2-3 minutes, until mixed well.
Add in the egg and beat again until well mixed.
Slowly add in the flour mixture.
Cover and refrigerate the dough for one hour.
Preheat the oven to 350 degrees.
Place the remaining 1/4 cup of sugar in a small bowl.
Roll dough into 1 inch balls and then place in the bowl of sugar. Roll them around in the sugar until they are fully coated.
Place on baking sheet and then using either your thumb, or the back of a 1/2 teaspoon, press down until you have an indentation into your cookie dough.
Add in your raspberry jelly into each "thumbprint" of the cookie. Bake at 350 degrees for 13-16 minutes.
To make the icing, combine all the ingredients listed above. Icing will be fairly thick. Then, drizzle the icing on top of the completely cool cookies and enjoy!
Store in an airtight container with parchment paper between the layers of cookies.