Using a hand mixer or a stand mixer fitted with the paddle attachment, cream the butter with the sugar and salt.
Add the vanilla extract and lavender paste and beat to combine. Add the flour and mix on low speed until dough forms.
Transfer dough onto a piece of plastic wrap and roll into a log, twisting the ends so that it's tightly wrapped. Chill in the refrigerator for at least 2 hours.
Preheat oven to 350°F and line a couple of baking sheets with parchment paper. Set aside.
Remove dough from the refrigerator, unwrap, and slice into ½ inch rounds. Arrange cookies on prepared baking sheets, a couple of inches apart, and bake for 18-20 minutes. Allow cookies to cool on baking sheet for 10 minutes, then transfer to a cooling rack to cool completely.
If you prefer to use lavender extract rather than paste, increase the amount to 1 tsp. The paste is more concentrated than the extract, so a little bit goes a long way.