In a medium bowl, combine flour, baking powder, and salt by whisking.

In a large bowl, beat butter, 1/2 cup granulated sugar, and 1 teaspoon vanilla extract until fluffy, about 2 to 3 minutes on medium speed. Add egg and beat until fully incorporated. Add flour mixture in increments, beating until just mixed. Refrigerate dough for exactly 1 hour.

Heat oven to 350°F (175°C). Prepare baking sheets by lining with parchment paper or silicone mats, or by greasing. Put the remaining 1/4 cup granulated sugar in a small dish. Shape dough into 1-inch balls, coat each in sugar, and place 2 inches apart on the baking sheets.

Create a depression in the center of each ball using your thumb, a rounded 1/2 teaspoon measuring spoon, or the handle end of a wooden spoon. Bake for 13 to 16 minutes, until edges are lightly browned. Move to wire racks.

In a small microwave-safe bowl, melt raspberry jam. Fill each cookie's indentation with jam.

Let cookies cool completely. For glaze, stir together confectioners' sugar, 1/2 teaspoon vanilla extract, and water until smooth; mixture should be thick. Drizzle over cookies.

Keep in an airtight container in a cool spot, layered with parchment paper between.