1. Combine cream, milk, honey, and salt in a medium saucepan. Cook over medium heat, stirring often, until it just reaches a bare simmer. Reduce heat to low.
2. Put yolks in a medium bowl. Drizzle 1/2 cup of hot cream mixture into eggs, whisking constantly. Whisk in rest of hot cream, 1/2 cup at a time. Pour mixture back into saucepan.
3. Cook over medium heat, stirring constantly with a wooden spoon, until mixture slightly thickens to the texture of heavy cream, 3 to 4 minutes.
4. Strain custard through a fine-mesh strainer into a clean bowl. Set bowl in a larger bowl of ice and cold water and let cool completely, stirring occasionally. Remove from ice bath, cover with plastic wrap, and chill at least 2 hours and up to overnight. (The colder it is, the faster it will freeze.)
5. Freeze custard in an ice cream maker according to manufacturer's instructions. Eat right away or, for a firmer ice cream, freeze at least 4 hours. Serve with Honey Roasted Figs spooned on top.