Grate oranges to get 1 tablespoon of zest.
After zesting, cut the oranges in half and squeeze out the juice into a measuring cup. You should have about ½ cup of orange juice. Set aside.
In the bowl of a stand mixer with the paddle attachment (or using a hand-held mixer), beat the butter and sugar together at medium speed until well blended, about 2 minutes.
Add the eggs one at a time, beating each egg until fully blended before adding the next.
Gradually add the orange juice and lemon juice to the butter mixture, beating at low speed just until blended.
Add orange zest. Stir until combined. The mixture might look curdled at this point, but that is okay!
Transfer the mixture to a small heavy-bottomed stainless steel saucepan.
Cook over medium heat, whisking constantly, for 14 to 16 minutes, or until the mixture thickens and reaches a temperature of about 170°F (77°C). Do not let it boil.
Transfer the cooked curd to a heat-safe bowl.
While the curd is still warm, set a piece of plastic wrap directly on top of it to prevent a film from forming on the surface.
Chill the orange curd in the refrigerator for at least 2 hours, or until firm.
Store the orange curd in an airtight container in the refrigerator for up to 2 weeks.