Place chicken in a large pot, cover with water, and bring to a simmer. Skim foam from the surface and add mirepoix and 2 bay leaves. Simmer for 2 hours. Strain, reserve broth, and let cool.
When cool, pull meat away from bones. Discard bones.
In a large stock pot, add olive oil and put on medium heat. Add onions, peppers, and garlic and lightly brown.
Add chicken, paprika, chili flakes, onion powder, garlic power, oregano, and 1 bay leaf. Sauté all together for about 5 minutes.
Add chopped tomato and remaining 2 bay leaves. Simmer for at least 2 hours or more, stirring vigorously to shred chicken. If your stew is getting dry, you can add some of the reserved broth. After 2 hours or so the chicken should be completely shredded and moist but not soupy. Season with salt and pepper. Reserve hot.
To roast bananas, split bananas in half lengthwise. In 2 pans, melt butter and put a pinch sugar. Add bananas cut side down in each pan and sauté until nicely browned. Flip bananas over and turn off heat, allowing bananas to cook a little more while the pan cools.
To serve, divide a nice portion of ropa vieja between 8 plates and garnish with olives, capers, and half a banana on each.