Start by taking butter out of the fridge about an hour before baking – you want it soft enough that your finger leaves an indent when you press it, but not so soft it’s melting.
In a medium bowl, whisk together flour, baking powder, and salt. This helps distribute the leavening evenly and prevents any salty pockets in your finished cookies.
In a large bowl (or your stand mixer if you’re using one), beat the softened butter until it’s smooth and creamy – about 30 seconds. Add the sugar and mix together until it’s light and fluffy, about 2-3 minutes. You’ll notice the color getting slightly lighter – that’s exactly what you want.
Add the eggs one at a time, beating well after each. Scrape down the sides of the bowl with a rubber spatula between additions. Mix in the lemon zest and vanilla until everything’s well combined.
Gradually add the flour mixture to your butter mixture, mixing on low speed just until combined. The dough will be soft but not sticky. Don’t overmix here or your cookies will be tough.
Wrap the dough in plastic wrap and chill for at least 30 minutes. This firms up the butter and makes the dough easier to roll out. You can leave it overnight if you want to break up the work.
When you’re ready to bake, preheat your oven to 350°F and line your baking sheets with parchment paper. Take the dough out while the oven heats up – it should be firm but still pliable.
Roll out the dough on a lightly floured surface to about 1/8 inch thickness. Cut with a 2-inch round cookie cutter, rerolling scraps as needed. Place cookies about 1 inch apart on your prepared sheets.
Bake for 12-14 minutes, rotating the pan halfway through. The cookies are done when the edges are just barely starting to turn golden and the centers are set but still pale. Don’t overbake – they should not be brown.