Place sugar, butter and salt in a stand or hand mixer with paddle attachment. Mix on medium speed until pale and fluffy, about 1-2 minutes, scraping sides midway. Add egg and lemon extract, mix until combined. Reduce speed to low and slowly add flour until combined. Dough should be thick and start sticking to paddle.
Place dough over a layer of plastic wrap, flatten into a disc about 1-inch thick and seal with more wrap. Place in fridge at least 1 hour to harden. If leaving in fridge longer, let sit at room temp about 30 minutes until soft enough to roll.
Remove plastic wrap and place dough on a flat, smooth lightly floured surface. Top with a large piece of plastic wrap and roll until ¼-inch thick. Discard wrap and use desired cookie cutter shape to cut out cookies.
Place cut-outs on a parchment or silicone lined baking sheet about 1-inch apart. Repeat process for leftover dough scraps.
Preheat oven to 350° F. Place cookies in freezer 10-15 minutes until dough is firm. Transfer to center of oven and bake for 5 minutes, rotate sheet and bake 5-6 minutes more, just until edges turn golden. Remove from oven, let sit 1-2 minutes then transfers cookies to wire rack until cool.
Repeat process if cookies do not all fit on one sheet. Enjoy as is, or decorate cookies with desired frosting and patterns.
Chilling the dough is important, follow the appropriate length of time at each step
Too much flour during rolling will create tough cookies
If making a large batch work with only a portion of the dough at a time. Keep extras in fridge until ready to roll
Start with cookie cutter at edge, then cut as close as possible to the previous cut-out for rest of dough. Re-roll remaining scraps and repeat process.
Cool to room temp before decorating
Sugar cookies are best fresh, but you can store in airtight container up to a week or freeze cookies for longer storage.