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- Place 2 tablespoons pistachios in food processor container. Cover; process until ground. Coarsely chop remaining pistachios. Set aside.
- Combine ground pistachios, 1 tablespoon thyme and steak seasoning; press evenly onto steaks. Brush mushrooms with oil.
- Place steaks in center of grid over medium, ash-covered coals; arrange mushrooms around steaks. Grill steaks and mushrooms, covered, 10 to 14 minutes (over medium heat on preheated gas grill, 12 to 16 minutes) for medium rare (145°F) to medium (160°F) doneness and until mushrooms are tender, turning occasionally.
- Carve steaks into slices. Season with salt and pepper, as desired; keep warm. Chop mushrooms. Combine mushrooms, rice, chopped pistachios and 1 tablespoon thyme in medium bowl; season with salt and pepper, as desired.
- Drizzle beef with some of Balsamic Syrup. Serve with rice mixture and remaining Balsamic Syrup. Garnish with thyme sprigs, if desired.