Preparation Heat 1 tablespoon oil in heavy large skillet over high heat. Add apple wedges; cook until beginning to brown, 2 to 3 minutes per side. Divide among plates. Reduce heat to medium-high. Add remaining 1 tablespoon oil and walnuts to skillet; stir 1 minute. Sprinkle walnuts with sugar; stir until walnuts and sauce are deep brown, about 30 seconds. Using slotted spoon, transfer walnuts to small bowl. Add shallots to skillet; stir until soft, 10 to 15 seconds. Stir in vinegar, then add escarole and radicchio to skillet. Sprinkle with salt and pepper and toss until beginning to wilt, about 1 minute. Season with salt and pepper. Mound salad on plates alongside apples. Top with cheese and walnuts.
Preparation Heat 1 tablespoon oil in heavy large skillet over high heat. Add apple wedges; cook until beginning to brown, 2 to 3 minutes per side. Divide among plates. Reduce heat to medium-high. Add remaining 1 tablespoon oil and walnuts to skillet; stir 1 minute. Sprinkle walnuts with sugar; stir until walnuts and sauce are deep brown, about 30 seconds. Using slotted spoon, transfer walnuts to small bowl. Add shallots to skillet; stir until soft, 10 to 15 seconds. Stir in vinegar, then add escarole and radicchio to skillet. Sprinkle with salt and pepper and toss until beginning to wilt, about 1 minute. Season with salt and pepper. Mound salad on plates alongside apples. Top with cheese and walnuts.