Brown Sugar Ice Cream with a Ginger-Caramel Swirl

In a medium heatproof bowl, whisk the yolks just to break them up, then whisk in half of the brown sugar (1/4 cup). Set aside. In a heavy nonreactive saucepan, stir together the cream, milk, salt, and the remaining brown sugar (1/4 cup) and put the pan over medium-high heat. When the mixture approaches a bare simmer, reduce the heat to medium. Carefully scoop out about 1/2 cup of the hot cream mixture and, whisking the eggs constantly, add the cream to the bowl with the egg yolks. Repeat, adding another 1/2 cup of the hot cream to the bowl with the yolks. Using a heatproof rubber spatula, stir the cream in the saucepan as you slowly pour the egg-and-cream mixture from the bowl into the pan. Cook the mixture carefully over medium heat, stirring constantly, until it is thickened, coats the back of a spatula, and holds a clear path when you run your finger across the spatula, 1 to 2 minutes longer. Strain the base through a fine-mesh strainer into a clean container. Set the container into an ice-water bath, wash your spatula, and use it to stir the base occasionally until it is cool. Remove the container from the ice-water bath, cover with plastic wrap, and refrigerate the base for at least 2 hours or overnight.