Put the peels in a food processor fitted with the steel blade. Add the sugar and process until the zest is very finely minced into the sugar. I let it rip for a full minute or so, scraping the bowl down once or twice.
In a stand mixer or in a bowl using an electric beater, cream the butter with the sugar and lemon peel mixture. Add the eggs, 1 at a time, and then add the lemon juice, salt and cornstarch, if using. Mix until combined. (Note: It’s going to look like a disgusting, curdled mess at this stage. Do not panic. I promise you it will come together and look delightful).
Pour the mixture into a 2 quart saucepan and cook over low heat until thickened (about 10 minutes), stirring constantly. Don’t walk away from it as you do this part or you will have lemony scrambled eggs. The lemon curd will thicken at about 170 degrees F, or just below simmer. Remove from the heat and strain into a bowl through a fine mesh sieve. Add to storage jars and allow to cool to room temperature before refrigerating. Curd will get thicker as it cools.
Use the cornstarch if you want a thicker curd, suitable for using as a filling in a layer cake.