In a medium-sized saucepan, bring the half-and-half to a gentle simmer over medium heat, stirring occasionally to prevent a skin from forming on top.
Meanwhile, vigorously whisk together the yolks, sugar and salt for around 30 seconds, then whisk in the lemon juice and zest in a large bowl. Keep whisking until the yolks are creamy and thick, which means the sugar has dissolved.
Once the cream reaches a gentle simmer, slowly pour or ladle it into the yolks while whisking. Turn the heat to low and return the mixture to the saucepan, scraping everything from the bowl with a spatula.
Using a spatula or wood spoon, stir the mixture for several minutes in a figure 8 motion, until the liquid has thickened slightly, approximately 5 minutes. If you want to use a thermometer, the temperature should read 165 degrees F.
Strain through a fine mesh strainer into a medium-sized bowl. Stir in the remaining 1/2 cup cream along with the vodka, if using. Cover with plastic wrap, pressing the plastic directly against the liquid to prevent a skin from forming.
Chill thoroughly, and then prepare in your ice cream maker according to manufacturer instructions.
Notes
Do not use bottled lemon juice in this recipe or the ice cream will have an unpleasant aftertaste.The vodka is entirely optional; it lowers the freezing point of the ice cream so it’s easier to scoop right out of the freezer.You can adjust the cream to milk ratio for a richer or lighter ice cream. Just keep the total amount of liquid the same.