In a large bowl, beat butter at medium-high speed with an electric mixer until creamy. Add thyme and lemon zest, beating well.
In another large bowl, sift together flour, cornstarch and salt. Add to butter mixture, beating at medium-low speed combine. Shape dough into a disk. Wrap tightly in plastic wrap. Refrigerate for 30 minutes.
Roll dough into 3 (1 1/2 inch thick) logs. Wrap tightly in plastic wrap, and refrigerate for 1 hour or up to 5 days. (Dough may be frozen for up to a month.)
Preheat oven to 350-degrees.
Line several baking sheets with parchment paper.
Bake until lightly golden, approximately 10 minutes. Transfer to a wire rack, and let cool completely. Store in an air tight container.
Cut shortbread dough into 1/4 inch slices. Place on prepared baking sheets.
Lavender Shortbread--substitute thyme with 2 tablespoons fresh lavender chopped.
While I have used both rosemary and lavender, I chose not to combine them in one cookie, instead making two batches, each with a different flavor. If you are feeling particularly adventurous, you may want to try tarragon, lemon balm, or even basil as your herb of choice in this recipe.