In the bowl of a stand mixer fitted with the paddle attachment, beat butter and granulated sugar at medium speed until creamy, about 2 minutes, stopping to scrape sides of bowl. Add chopped thyme, lemon zest and juice, and salt, beating to combine. With mixer on low speed, gradually add flour, beating until a dough forms. Wrap dough in plastic wrap, and refrigerate for 30 minutes.

Preheat oven to 350°. Line 2 large rimmed baking sheets with parchment paper.

On a lightly floured surface, roll dough to ¼-inch thickness. Using a 2-inch fluted round cutter, cut dough, rerolling scraps as necessary. Place on prepared pans. Place a thyme sprig on each cookie, gently pressing into dough; sprinkle with sanding sugar.

Bake until light golden brown, 10 to 12 minutes, rotating pans halfway through baking. Let cool completely on wire racks.