Prepare the Chicken: Season the chicken breasts with salt and black pepper on both sides. In a large pot or deep skillet, heat the olive oil over medium-high heat. Add the chicken breasts and sear them until golden brown, about 4-5 minutes per side. Remove the chicken from the pot and set aside.
Sauté the Vegetables: In the same pot, add the minced garlic and cook until fragrant, about 1 minute. Add the julienned onions, green bell pepper, and red bell pepper. Sauté the vegetables until they start to soften, about 5-7 minutes.
Add Tomatoes and Broth: Stir in the diced fresh tomatoes and canned tomatoes, mixing well with the sautéed vegetables. Pour in the chicken broth and add the bay leaves. Bring the mixture to a simmer.
Combine Chicken and Serrano Ham: Return the seared chicken breasts to the pot, nestling them into the vegetable mixture. Add the sliced serrano ham, distributing it evenly throughout the pot.
Simmer and Cook: Reduce the heat to low and cover the pot. Let the chicken and vegetables simmer for about 25-30 minutes, or until the chicken is cooked through and tender, and the flavors are well combined. If the sauce is too thin, you can remove the lid during the last 10 minutes to let it thicken slightly.
Serve: Once cooked, remove the bay leaves and discard them. Serve the Chicken Chilindrón hot, with the sauce and vegetables generously spooned over each chicken breast. This dish pairs well with rice, crusty bread, or boiled potatoes.