Preheat oven to 375°F. Spread 1/4 cup enchilada sauce on the bottom of an 8-inch round cake pan.
Spread 1 tortilla with one-third of the refried beans. Place it bean side up in the cake pan. Top with one-third of the chicken (1 cup), 1/4 cup chopped onion, and 1/2 cup shredded cheese. Spoon about 2/3 cup of the enchilada sauce over the top.
Repeat the layering two more times: tortilla, beans, chicken, onion, cheese, sauce.
Finish with the final tortilla. Bake uncovered until bubbling and hot throughout, about 20 to 25 minutes.
Turn oven to broil. Sprinkle top with the remaining 1/4 cup cheese and broil until melted, 1–2 minutes.
Let rest for 10 minutes before slicing. Garnish with remaining chopped onion and fresh cilantro before serving.