In a medium mixing bowl, beat together the softened butter, fine sea salt, vanilla extract, and powdered sugar on medium speed until smooth and creamy, about 2-3 minutes. Gradually add raspberry powder and whole milk to desired consistency, mixing until combined. Set aside.

Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.

In a stand mixer, combine the softened butter, granulated sugar, powdered sugar, fine sea salt, vanilla extract, and lemon zest. Beat until fluffy and pale, about 4-5 minutes.

Crack in the large egg and mix for an additional 2 minutes until fully incorporated.

Gradually add all-purpose flour and baking soda, mixing on low speed until just combined.

Portion out about 3 tablespoons of dough, roll into balls, place on baking sheets, and flatten slightly with a floured measuring cup.

Bake for 12 minutes, or until the edges are golden and the centers appear set. Allow to cool on the baking sheet for around 5 minutes before transferring to a wire rack.

Frost with about 1 tablespoon of raspberry buttercream on each cookie after they cool completely. Optionally, sprinkle additional raspberry powder or colorful sprinkles over the frosting.