Using a vegetable peeler, remove the peel from the lemons in long strips. Place the lemon peels in a 2-quart pitcher.

Pour the vodka over the peels and cover with plastic wrap. Steep the lemon peels in the vodka for 3 to 4 days at room temperature.

For the syrup, stir the half and half, vanilla extract, and sugar in a large saucepan over medium-low heat. Stir frequently until the sugar completely dissolves, about 5 minutes. Do not boil the mixture.

Remove from heat and cool completely to room temperature.

Discard the lemon peels from the limoncello base, and stir in the cooled syrup.

Transfer the limoncello to bottles. Seal the bottles and refrigerate until cold, and serve. You can freeze bottles for up to 3 months.