In a food processor, pulse flour, confectioners' sugar, salt and lemon zest until combined. Add butter and process until sandy. Add egg yolks and lemon juice; pulse until dough comes together. Divide dough in half and form each into a 1 ½ inch-wide log. Wrap in plastic and freeze until firm, about 2 hours (or up to 1 month).
Preheat oven to 350°F. Spread granulated sugar on a piece of parchment paper and roll logs over sugar to coat. Slice logs into ¼ inch thick slices and arrange 1 inch apart of a parchment lined cookie sheet. Bake until cookies are golden brown around the edges, about 12 minutes, rotating the sheet halfway through cooking time. Cool cookies on a wire rack. Store in airtight container at room temperature up to 5 days.
For the Frosting:
In a small bowl mix all frosting ingredients until fluffy. Frost cooled cookies.
Notes
Cookie: Adapted from a recipe by Martha StewartFrosting: Adapted from Land-O-Lakes Lemon Meltaway recipeNutrition information is calculated using an ingredient database and should be considered an estimate. When multiple ingredient alternatives are given, the first listed is calculated for nutrition. Garnishes and optional ingredients are not included.