Combine first 3 ingredients in a 3-quart heavy-bottom saucepan over medium-high heat. Bring to a simmer, stirring constantly until sugar dissolves. Remove from heat.
Pour water to a depth of 1 inch into bottom of a double boiler over medium heat; bring to a boil. Reduce heat, and simmer; place egg yolks in top half of double boiler. Slowly whisk in hot half-and-half mixture. Cook, whisking constantly, 6 minutes or until mixture reaches 160° and thickens enough to coat the back of a spoon.
Remove from heat; strain through a fine wire-mesh sieve to remove any lumps, if necessary. Stir in heavy cream. Whisk in olive oil. Refrigerate until completely cold.
Freeze in an ice-cream maker according to manufacturer's directions.