Combine garlic, thyme and pepper; press evenly onto beef steaks. Set aside.
Brush mushrooms with oil. Place steaks in center of grid over medium, ash-covered coals; arrange mushrooms around steaks. Grill steaks, uncovered, 11 to 14 minutes (over medium heat on preheated gas grill, covered, 9 to 14 minutes) for medium rare (145°F) to medium (160°F) doneness, turning occasionally. Grill mushrooms 16 to 18 minutes (over medium heat on preheated gas grill, covered, 12 to 15 minutes) or until tender, turning occasionally.
Meanwhile, combine Blue Cheese Butter ingredients in small bowl until well blended.
Cover and refrigerate 2 steaks, 4 mushrooms and 1/2 cup Blue Cheese Butter to use in Ribeye Steak Sandwiches. Spread remaining Blue Cheese Butter over remaining 2 steaks. Coarsely chop remaining 4 mushrooms; divide evenly among 4 plates. Carve steaks into slices; arrange evenly over mushrooms. Season with salt, as desired. Garnish with parsley, if desired.
Ribeye Steak Sandwiches: Toast eight 1/2-inch thick slices olive bread. Spread 1 tablespoon leftover Blue Cheese Butter on 1 side of each bread slice. Carve leftover grilled steaks into slices; season with salt and pepper, as desired. Divide slices evenly among buttered sides of 4 bread slices.Top each with 1 leftover grilled mushroom. Divide 1-1/2 cups fresh baby spinach evenly over mushrooms. Close sandwiches with remaining bread slices, buttered sides down. Cut sandwiches in half; serve.