Marinate the chicken. Combine the grated onion with olive oil, garlic, lemon juice, oregano, paprika, salt, and pepper. Toss the chicken with the marinade, turning to coat. Let sit for at least one hour, preferably overnight.
Preheat oven to 425 degrees.
Make the spicy harissa sauce. Place 1 red bell peppers and 3 fresno chilies on a baking sheet. Roast the peppers and chili for 20 minutes or until charred, turning halfway through. Transfer the vegetables to a heat safe bowl and wrap with plastic wrap. Let sit for 10 minutes. Remove the lid and carefully remove the skin and discard the stem and seeds.
Blend the bell pepper and fresno with olive oil, lemon juice, garlic, caraway, coriander, and cumin until smooth. Season with salt and pepper and let cool completely.
Make the hummus. Drain the chickpeas, reserving ¼ cup of the canned liquid. Blend together the chickpeas with the reserved liquid, tahini, lemon, and garlic until smooth. Slowly add the olive oil while the blender is running and blend until smooth. Season with salt and pepper and set aside.
Make the garlic yogurt sauce. Whisk together the yogurt with garlic, and lemon juice. Season with salt and pepper and let sit for at least 30 minutes.
Prepare the remaining toppings. Place the remaining red bell pepper and green bell pepper on a baking sheet. Roast in the oven for 20 minutes or until charred, turning halfway through. Transfer the vegetables to a heat safe bowl and wrap with plastic wrap. Let sit for 10 minutes. Remove the lid and carefully remove the skin and discard the stem and seeds. Slice the peppers and set aside.
Season the carrot with 1 tablespoon olive oil, salt, and pepper and wrap in aluminum foil. Place the wrapped carrot on a baking sheet. Roast the carrot for 30-35 minutes or until tender. Slice the carrot into thin slices and set aside.
Remove the chicken from the marinade, scraping off the excess. Heat 1 tablespoon oil in a saute pan over medium heat and cook the chicken until browned and the juices run clear. Remove from heat and let rest for 10 minutes. Chop the chicken into small pieces.
Assemble the doner kebab sandwich. Toast the bread and slice in half. Smear a good amount of hummus on the bottom bread followed by the garlic yogurt. Smear the spicy harissa on the top bread.
Top the bottom bread with chicken followed by the roasted peppers, sliced carrots, red onion, tomato, cucumber, shredded lettuce, feta, mint, and parsley. Sprinkle sumac on top and serve immediately.