Heat 2 tablespoons vegetable oil in a large skillet over medium heat.
Add the chopped onion, minced garlic, and diced jalapeño; cook until softened, about 3–4 minutes.
Stir in 1½ teaspoons chili powder, 1 teaspoon cumin, ¼ teaspoon cinnamon, and 1 teaspoon salt and cook briefly to bloom the spices.
Add the chopped tomato and 2 teaspoons chopped cilantro; cook 2–3 minutes until the tomato softens.
Stir in 2 cups shredded rotisserie chicken and ¼ cup sour cream; cook until heated through and well combined.
Spoon a few tablespoons of refried beans down the center of each warmed 10-inch tortilla.
Top each with about 1/6 of the chicken mixture and ¼ cup shredded Monterey Jack cheese.
Fold the sides of each tortilla toward the center and roll into a tight burrito shape; secure with toothpicks if needed.
Pour 1–2 inches of oil into a heavy pot and heat to 350°F (175°C). Fry 1–2 chimichangas at a time for 3–4 minutes, turning once, until golden brown.
Drain on paper towels and remove toothpicks. Serve hot with shredded lettuce, chopped tomatoes, sour cream, fresh cilantro, and additional cheese as desired.