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.
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.
Cook over medium heat, stirring constantly with a wooden spoon, until mixture slightly thickens to the texture of heavy cream, 3 to 4 minutes.
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.)
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.