Preheat oven to 325°F with the rack in the middle position.
In a food processor, add the flour, sugar, salt, and lemon zest. Pulse together a few times to mix.
Add the butter chunks around the flour along with the lemon juice. Pulse again until the dough starts to come together. Do not over process. It should still look crumbly. The dough should stick together when squeezed. If too dry, add a little more water or lemon juice and briefly incorporate.
Dump the dough onto a large sheet of parchment paper. Start pressing it together into a log shape, and roll up the paper around it to help make it into a log. Twist the ends and place in the refrigerator to chill for 30 minutes.
Remove the dough log from the paper and using a serrated knife, slice the dough into ½ inch (or thinner) pieces.
Place the cookies on a silicone mat or parchment lined baking sheet. Bake approximately 20 minutes, until the bottom edges that touch the baking sheet are just starting to turn a golden brown.
Remove the cookies from the oven. Place the cookies on a wire rack to cool.
If desired, dunk or drizzle with the lemon glaze when the cookies are cool. Sprinkle with more lemon zest on top of the wet glaze to set. Store in an airtight container for up to two weeks.
You can also make this by hand by pinching the butter into the flour mixture, or using a pastry cutter or fork. If it gets too warm from your hands, chill for a few minutes before continuing.If you want to make these in a square pan and cut them into triangles or rectangles, follow instructions for Lemon Lavender Shortbread Cookiesafter making the dough.