Heat 1 tablespoon olive oil in a saute pan over medium heat. Add chicken breasts, skin side down. Cook until golden brown, about 4 minutes per side.
Meanwhile, heat 2 tablespoons olive oil a second saute pan. Add chile and coriander; saute 1 minute. Add red onion, beets, mustard seeds, and salt, and cook for 1 minute. Add carrots and 1 tablespoon vinegar; season with pepper. Saute for 3 to 4 minutes, stirring occasionally.
Add collard greens to vegetable mixture, and cook until wilted, 3 to 5 minutes.
In a medium bowl, toss mustard greens with 1 tablespoon olive oil and 1 tablespoon vinegar; season with salt and pepper. Pour vegetable mixture on top of the greens, and toss quickly, allowing the greens to wilt slightly. Divide among 2 plates.
Add quince jam to chicken breasts, basting occasionally with melted jam. Season with salt and pepper. Add white wine, sambal oelek, the remaining 1 tablespoon vinegar, and 1 teaspoon oil; stir to combine. Simmer for 4 minutes. Add olives, and cook until just heated, about 30 seconds.
Place a chicken breast on top of vegetables, and pour any pan juices over chicken. Serve immediately.