Beat the butter and sugar together in the bowl of a stand mixer until light and fluffy.
Add the egg and beat until well blended.
Make sure your rosemary is very finely chopped – use an electric spice grinder if you have one. If not, chop as much as possible with a heavy knife.
Add the rosemary and lemon zest to the bowl and beat until blended. Add the flour and salt and beat until combined and smooth.
Scoop half the dough onto a long piece of plastic wrap and shape into a log.
Roll up the dough and wrap tightly into a small, thin log. I like to make these as small bites, so I roll the log about 1-inch in diameter.
Repeat with the remaining dough. Refrigerate the logs for at least an hour but these will keep in the fridge for several days.
When ready to bake, preheat the oven to 350 degrees.
Line a baking sheet with parchment paper. Remove the dough from the fridge and slice wafers, about 1/8 of an inch thick, from the logs.
Lay them on the baking sheet about ½ an inch apart and bake for 5 minutes, just until the centers are firm and the edges are slightly brown.
Remove to wire racks to cool completely.