How to Make It
Preheat oven to 400°F. Toss together figs, 1 tablespoon olive oil, and 1/4 teaspoon salt on a rimmed baking sheet. Bake in preheated oven until figs are slightly caramelized and soft, about 20 minutes.
Heat remaining 1 tablespoon olive oil in a medium saucepan over medium. Add chopped leeks, and cook until soft, about 1 minute. Add sake and mirin, and cook, stirring often, until liquid is reduced by half, about 2 minutes. Reduce heat to low. Stir in miso, and cook, stirring often, until mixture thickens and darkens in color, about 5 minutes. Remove miso mixture from heat.
Using a fork, break cooked figs apart, removing stems. Combine figs, miso mixture, and balsamic vinegar in a food processor. Pulse until mostly smooth, about 20 times. Set aside.
Preheat grill to very high (550°F to 600°F). Season rib eye with pepper and remaining 3/4 teaspoon salt. Place on oiled grates; grill, covered, until a meat thermometer registers 130°F, about 4 minutes per side. Remove from grill, and let rest 5 minutes. While steak rests, heat fig miso over low. Slice beef, and serve with fig miso.