Preheat a grill to medium high. Pierce the sweet potatoes all over with a fork and microwave until almost tender, 5 to 6 minutes; let cool. Halve lengthwise and set aside.
Meanwhile, heat 1 tablespoon vegetable oil in a medium saucepan over medium heat. Add the shallot, ginger, garlic, cayenne, 1/2 teaspoon salt and 1/4 teaspoon black pepper and cook, stirring, until the shallot softens, about 3 minutes. Stir in the tomato paste and cook until darkened, about 1 minute.
Transfer the tomato mixture to a blender; add the sunflower seed butter, cilantro and 2/3 cup water and puree, adding more water to loosen if necessary. Season with salt and black pepper.
Oil the grill grates. Brush the sweet potatoes and bell peppers with the remaining 1 tablespoon vegetable oil; season with salt and black pepper. Toss the chicken with 1/4 cup of the sunflower seed butter sauce; season with salt. Grill the chicken, turning, until marked and cooked through, 10 to 12 minutes. Grill the sweet potatoes and bell peppers, turning, until marked and tender, 5 to 8 minutes. Serve the chicken with the vegetables and remaining sauce. Top with cilantro.