Heat your oven to 300°F. Line an 8-inch square or 9-inch round cake pan with parchment paper. No need to grease.
In a stand mixer: Beat butter, sugar, and salt together, scraping frequently, until butter is soft. Add flavoring of choice and flour, and mix just until combined.
In a food processor: Combine powdered sugar, salt, and flour in the work bowl, pulsing a few times. Add flavoring of choice and butter and pulse several times to chop the butter down into smaller pieces. Then, run the machine until it is fully incorporated, coming together in a smooth mass.
Add to baking pan in chunks. Use hands to press evenly into the pan, then an offset spatula to smooth the top.
Bake for 20 minutes, then remove from the oven to cut into shapes. Leave oven on.
Shape the cookies: For the 8-inch square pan, cut into 3 columns and 8 thin bars. Use the back of a wooden skewer to drag across the surface, making slightly indented lines first, then use a very thin, sharp paring knife to cut along these lines.
For a 9-inch round pan, use a 2 to 3-inch round cookie cutter to cut the center. Then, use the back of a wooden skewer to gently indent lines from the inner circle to the outer edge of the cookie.
Return to the oven for another 25 to 35 minutes, until cookies have a deep golden edge but are mostly pale across the top.
Let cool in pan, or remove after 10 minutes if impatient.
