In the bowl of a standing electric mixer, beat butter, 3/4 cups sugar, salt, thyme, and lemon zest until light and fluffy. Add the flour and mix until the dough comes together.
For immediate baking, roll the dough into 1½-inch balls and place on parchment-lined baking sheets. Gently flatten the dough with fork tines dipped in 1-2 tablespoons granulated sugar (to prevent sticking). Bake in an oven preheated to 300° F for about 20 minutes, until the bottom edge of the cookies show only the slightest tinge of pale gold. Transfer cookies to a cooling rack.
To create a more elaborate pattern on your cookies, dip the dough balls in 1 to 2 tablespoons granulated and press them flat with the bottom of an interestingly-patterned crystal glass or bowl. Freeze cookies for 30 minutes to set the design. In an oven preheated to 300° F, bake for 20-22 minutes, until the bottom edge of the cookies show only the slightest tinge of pale gold. Transfer cookies to a cooling rack.