In a small saucepan over medium heat, melt butter and stir frequently. Butter will begin to foam and boil. After 4 to 5 minutes you will see brown flecks appear in the bottom of the pan. Continue to stir until butter is golden and flecks are a medium brown color. Watch closely, butter will brown quickly. Process will take about 5 to 7 minutes.
Remove butter from heat and pour into a bowl. Refrigerate for 15-25 minutes, or until butter is cool and solidified. You're looking for a room temperature or slightly cooler, solid butter.
In a bowl, cream together butter and sugar. Add vanilla and stir to combine.
In a separate bowl, sift (or whisk) together flour* and salt. Add dry ingredients to butter mixture and mix until a dough forms. Dough will be crumbly, but will hold together when pinched between two fingers.
Toss dough out onto wax or parchment paper and form into two logs, about 1 1/2" wide. Refrigerate for an hour (up to 24 hours).
Preheat oven to 350 degrees. Line a baking sheet with parchment paper and set aside.
Remove dough from refrigerator and unwrap. Using a sharp knife, slice dough into 1/4 inch slices. On a sheet of wax paper or parchment, pour a small amount of turbinado sugar. Roll the edges of each cookie in sugar and place 2 inches apart on prepared baking sheet.
Bake for 12-14 minutes or until cookies just begin to lightly brown around edges. Remove from oven and allow to cool for 2-3 minutes before removing from sheet to cool completely.
*Your dough will look crumbly - this is normal. Test your dough. Try pinching some dough between two fingers - does it hold together? If so, your dough is the correct consistency.If your dough is sticky, add 1/4 cup more flour. And if your dough is dry and not holding together, add 1 tablespoon of water.For shortbread, I often suggest leaving out 1/4 cup of flour. Combine the rest and see how your dough looks. If you need to add more, you can.
Your cookies will keep for 5-7 days in a sealed container. To help keep cookies fresh, you can place a slice of bread in the container with the cookies. Replace the bread slice as needed.
You can keep raw cookie dough in the refrigerator for 3 days. Cookie dough and baked cookies freeze well, up to 3 months in a sealed plastic container or freezer bag. Allow frozen dough to thaw for up to 10 minutes on the baking sheet before baking, or add 1-2 minutes to the baking time.