Step 1Wash the tangerines. Remove the peel from 1 tangerine with a vegetable peeler, being very careful not to take any of the white pith. Put it with the sugar and half-and-half in a nonreactive saucepan and heat just to boiling. Remove from the heat and let steep for 5 to 10 minutes.
Step 2Whisk the egg yolks in a bowl to break them up and pour the warm half-and-half mixture into them, whisking constantly. Return the mixture to the pan and cook over low heat, stirring constantly, until the custard coats the back of a spoon, about 2 to 3 minutes.
Step 3Pour through a strainer into a bowl and grate the rind of 2 more tangerines into the custard. Grate as fine as possible and let stand in the warm custard a few minutes. Juice the tangerines -- you will want 5 to 6 tablespoons.
Step 4Add the cream, the tangerine juice and a few drops of vanilla extract to the custard. Chill. This can all be done a day before you want to freeze the ice cream; refrigerate the mixture, tightly covered.
Step 5Freeze in an ice cream maker according to manufacturer's instructions; pack into an airtight container and freeze.