Bring a pot of lightly salted water to a rapid boil over medium-high heat. Add the chicken breasts to the boiling water, cover the pot, and cook for 15 to 20 minutes. Drain the chicken and set it aside.

Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 10x15 inch baking dish.

In a skillet, melt the butter over medium heat. Add the chopped onion, green bell pepper, and red bell pepper, and cook until they are just softened, about 5 to 8 minutes. Transfer the cooked vegetables to a large bowl.

Add the cooked chicken, shredded Cheddar cheese, diced green chile peppers, green salsa, chopped fresh cilantro, ground cumin, and chopped chipotle peppers in adobo sauce to the bowl with the vegetables. Season with salt and ground black pepper to taste, then mix everything together thoroughly.

Spoon about 1/3 cup of the chicken mixture along the edge of each flour tortilla. Roll each tortilla tightly into a tube shape and place them seam-side down in the prepared baking dish. Continue until all the chicken mixture is used.

Sprinkle the shredded Monterey Jack cheese evenly over the rolled enchiladas.

In a small bowl, whisk together the whipping cream and chicken broth. Pour this mixture evenly over the enchiladas in the baking dish.

Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.

Remove the foil and continue baking until the cheese is completely melted, about 10 minutes more.