In a large bowl with a hand mixer or in the bowl of a stand mixer, cream the butter with the sugar until light and fluffy, about 2 minutes. Then, add in the vanilla and the egg.
Add in the flour and mix gently until the dough is combined. Then, add in the lemon zest and rosemary.
Split the dough into two pieces and roll into balls. Then, roll the balls into logs and cover them in plastic wrap. Let the logs of dough sit in the fridge for an hour.
While the logs are chilling, preheat the oven to 350 degrees and prepare a cookie sheet with parchment paper. Set it to the side.
When the cookie dough is firm, take it out of the fridge. Use a sharp knife to slice the cookie dough into ¼-inch size pieces. Roll the edges of the cookie dough into the coarse sugar and place them on the prepared baking sheet.
When the cookies are set on the baking sheet, place them in the oven and let them bake for about 15 minutes. The cookies should have a slight gold coloring and be firm around the edges.
Let the cookies slightly cool on the baking sheet before removing them to a cooling rack.
