In a large bowl, whisk egg yolks until combined; set aside.
In a 4-quart Dutch oven, combine whipping cream, milk, brown sugar, honey and ginger. Cook over medium heat, stirring frequently, just until tiny bubbles form around the edge. Reduce heat to low and cook, stirring frequently, for 10 minutes more to infuse the honey and ginger flavors into the cream mixture.
Gradually whisk 2 cups of the hot whipping cream mixture into the egg yolks; return mixture to saucepan. Cook cream and yolk mixture over medium-low heat, stirring constantly with a wooden spoon, just until the mixture thickens enough to coat the back of a wooden spoon (about 5 minutes). (The mixture should be thick enough to leave a smooth, creamy layer that clings to the surface of the wooden spoon.) Remove from heat.
Strain the mixture through a fine mesh sieve. Cover the surface of the mixture with plastic wrap. Chill in an ice bath or chill in the refrigerator at least 4 hours.
Freeze and ripen in a 4- to 5-quart ice-cream freezer according to manufacturer's instructions. Makes 2 quarts (16, 1/2-cup servings).