Cream together butter and sugar in the bowl of an electric mixer until light and fluffy, about 5 minutes.
Add lemon zest, rosemary, lemon paste, and vanilla. Beat for an additional minute.
Add eggs. It will look curdled, but once the flour is added, it will all come together.
Add flour, baking powder, and salt. Mix until fully incorporated, but being careful not to overmix.
Turn dough out and wrap in plastic wrap. Chill for at least 2 hours, or overnight.
Preheat oven to 350° and line baking sheets with parchment paper.
Roll dough out onto a floured surface and use your favorite cutters to cut into shapes.
Bake for 8 to 10 minutes or until set, but do not brown. Let cool on baking sheets.
Use your favorite glaze or royal icing recipe to decorate.