Grate zest from the lemons. You will need 1 tablespoon of zest.
After zesting, cut the lemons in half and squeeze out the juice into a measuring cup. You should have about ½ cup of lemon juice.
In the bowl of a stand mixer (or in a bowl and using a hand-held mixer) beat butter and sugar at medium speed until blended (about 2 minutes).
Add eggs to the mixture, one at a time, beating each egg until it's blended before adding the next.
Gradually add the lemon juice to the butter mixture, beating at low speed just until blended.
Remove the bowl from the mixer and stir in the lemon zest by hand. The mixture might look curdled at this point, but that's okay!
Transfer the mixture to a small heavy-bottomed stainless steel saucepan.
Cook over medium-low heat, whisking constantly, for 16 to 20 minutes, or until the curd thickens enough to coat the back of a spoon. Then, transfer to a heat-safe bowl. (You may not want to use a wire whisk as it could react to the acid in the curd.)
While the mixture is still warm, set a piece of plastic wrap directly on top of the lemon curd to prevent a film from forming on the surface.
Chill the lemon curd in the refrigerator for at least 2 hours, or until firm.
Store the lemon curd in an airtight container in the refrigerator for up to 2 weeks.