Preheat oven to 350 °F.
In your mixing bowl beat room temperature butter until it is creamy.
Add the sugar and mix thoroughly.
Add thyme, lemon zest, vanilla extract, lemon extract, and salt and continue to mix until ingredients combine.
Add the flour 1 cup at a time until the mixture just starts to come together.
Create a ball of dough and flatten it slightly before wrapping it in plastic wrap and chilling it for 1 hour.
Remove dough from refrigerator.
Lightly flour your surface and roll the dough out to 1/4 inch thick.
Use cookie cutter to cut out cookies.
Place cookie cut-outs on a parchment paper covered baking sheet.
Place cookies in the refrigerator for 20 minutes.
Remove from refrigerator and bake for 8 - 10 minutes, or until cookies are golden brown.
Let the cookies cool completely and then ice them.
Let icing harden before serving.