Preheat oven to 325°F.
Make the glaze: combine ½ cup California Figs, Dijon, grainy mustard, and honey in a food processor or blender. Process well—the mixture will have some chunks in it. Set aside.
Place the ham into a large baking dish. Add the carrots.
Slather the glaze over the ham. Sprinkle with brown sugar, pressing it into the sides of the ham.
Top the carrots with the remaining California Figs.
Drizzle the juice around the bottom of the pan.
Seal tightly with foil and bake for 1 hour (15 minutes per pound).
Remove the ham and place it in a serving dish. Strain the sauce from the baking dish into a gravy boat to serve alongside. Nestle the carrots and figs drizzled with pan juices along the side of the serving dish.