Cream together granulated erythritol and butter.
Beat in vanilla, eggs, baking powder, salt, and flour.
Chill for 20-30 minutes, then roll out to 1/8" to 1/4" thick.
Use cookie cutters to cut your shapes.
Bake at 375 for 8-10 minutes.
For the frosting, combine 6 tbsp butter, 1/4 cup coconut milk, lemon extract, and powdered erythritol.
Add dye and frost cookies once they're cooled.