Heat oven to 400 degrees. Scrub sweet potato, and prick with a fork. Bake until tender, about 40 minutes. Remove from oven, and peel when cool enough to handle. Transfer to a large bowl, mash, and set aside.
Meanwhile, rinse millet. Bring 2 1/2 cups water to a boil; add millet and 1 teaspoon salt. Cover, reduce heat to medium low, and simmer until all the water is absorbed, about 15 minutes. Remove from heat, and add to mashed sweet potato; mix to combine.
Place carrot and celery in a food processor; pulse to chop finely. Transfer from processor to a small bowl. Pulse onion and garlic until finely chopped, and add to carrot and celery. Heat 2 teaspoons sesame oil in a skillet over medium-low heat. Add garlic, onions, celery, and carrots; cook until onions are translucent, about 7 minutes. Add to millet mixture; stir to combine.
Bring a small saucepan of water to a boil. Add 1 teaspoon salt and peas; cook until tender but still firm, about 3 minutes. Drain; transfer peas to a bowl of ice water for 1 to 2 minutes. Drain again, and combine with chickpeas in a food processor; pulse to chop medium-fine. Add to millet mixture.
Add coriander, cumin, fennel, cayenne, flour, sunflower seeds, lemon juice, chives, parsley, remaining 1 1/2 teaspoons salt, and pepper. Mix well, and form into 8 patties.
Heat 2 teaspoons sesame oil in a nonstick skillet over medium heat. Add four patties, and cook until golden brown and heated through, 7 to 8 minutes per side. Keep warm in a low oven; repeat with remaining 2 teaspoons oil and patties.
Serve immediately with sprouts and tahini sauce on buns brushed with olive oil and toasted.