PreparationFor chicken: Whisk onions, mustard, lemon juice, and garlic in medium bowl to blend. Using fingertips and leaving 1 side still attached, loosen skin on each chicken thigh. Lift skin flap on each and fold back. Spoon half of mustard seasoning atop thighs, dividing equally; spread to cover meat. Fold skin flap over to enclose seasoning and secure skin with metal pin. Sprinkle thighs with salt and pepper on both sides. Turn thighs, skin side up, and spread remaining mustard seasoning over skin. Transfer to small baking sheet. DO AHEAD: Chicken can be prepared 6 hours ahead. Cover and refrigerate. Prepare barbecue (medium-high heat). Preheat oven to 250°F. Brush grill rack generously with olive oil grill chicken until golden brown and cooked through, turning chicken occasionally and moving to cooler spot on grill if browning too quickly, 40 to 50 minutes. Transfer grilled chicken to another baking sheet; keep warm in oven while preparing polenta. For polenta: Bring 5 cups water to boil in heavy large saucepan over high heat. Gradually whisk in polenta, then 1 1/2 teaspoons coarse salt and sugar. Reduce heat to medium-low; simmer until polenta is tender, thick, and creamy, whisking often and adjusting heat to maintain gentle simmer, 25 to 30 minutes. Add corn kernels and cook, stirring constantly, until corn is tender, about 5 minutes. Mix in mascarpone cheese. Season polenta to taste with salt and pepper. Spoon polenta onto each of 6 plates. Top with grilled chicken and serve.
PreparationFor chicken: Whisk onions, mustard, lemon juice, and garlic in medium bowl to blend. Using fingertips and leaving 1 side still attached, loosen skin on each chicken thigh. Lift skin flap on each and fold back. Spoon half of mustard seasoning atop thighs, dividing equally; spread to cover meat. Fold skin flap over to enclose seasoning and secure skin with metal pin. Sprinkle thighs with salt and pepper on both sides. Turn thighs, skin side up, and spread remaining mustard seasoning over skin. Transfer to small baking sheet. DO AHEAD: Chicken can be prepared 6 hours ahead. Cover and refrigerate. Prepare barbecue (medium-high heat). Preheat oven to 250°F. Brush grill rack generously with olive oil grill chicken until golden brown and cooked through, turning chicken occasionally and moving to cooler spot on grill if browning too quickly, 40 to 50 minutes. Transfer grilled chicken to another baking sheet; keep warm in oven while preparing polenta. For polenta: Bring 5 cups water to boil in heavy large saucepan over high heat. Gradually whisk in polenta, then 1 1/2 teaspoons coarse salt and sugar. Reduce heat to medium-low; simmer until polenta is tender, thick, and creamy, whisking often and adjusting heat to maintain gentle simmer, 25 to 30 minutes. Add corn kernels and cook, stirring constantly, until corn is tender, about 5 minutes. Mix in mascarpone cheese. Season polenta to taste with salt and pepper. Spoon polenta onto each of 6 plates. Top with grilled chicken and serve.