Add tomatoes to a pot of boiling water for about 10 minutes until skin loosens. Peel skin and discard seeds using a strainer, saving only the pulp and juices.
Add tomato pulp to a medium saucepan with heavy whipping cream and milk, and allow the mixture to simmer. In a separate bowl, combine egg yolks with sugar. Reduce heat to low and slowly whisk egg yolk mixture into the simmering tomato liquid, constantly whisking for about 5 minutes until the mixture has thickened slightly. Remove from heat and whisk in vanilla, orange liqueur, and salt.
Pour the mixture into a bowl and cover, cooling for 2–12 hours before freezing. For the best result, use an electric ice-cream maker to complete your ice cream, per the manufacturer’s instructions. If you don’t have access to an ice-cream maker, pour the mixture into a hard container, such as a deep pot or pan; cover; and freeze for at least 6 hours before serving. Serve with candied basil leaves (it is okay if they crumble).
