Combine the sugar, water, and corn syrup in a small saucepan and bring to a boil. Cook until the temperature reaches 238°F on a candy thermometer (soft ball stage).

Meanwhile, beat the egg yolks with an electric mixer until thick and pale yellow. Continuing to beat the egg yolks on medium speed, slowly pour in the sugar syrup in a fine, steady stream.

Beat until the mixture cools to room temperature, about 7 minutes. Stir in the zest and half-and-half.

Cover and refrigerate until thoroughly chilled, about 3 hours.

When ready to freeze, stir in the cream. Freeze in an ice cream maker according to the manufacturer’s instructions.

When the ice cream is almost frozen, spoon in the Strega and churn until blended in, about 1 minute more.

Transfer to a container, cover, and freeze until firm, about 2 hours.