Grill poblano pepper until skin is blistered and slightly blackened. Remove from heat until cool enough to handle. Remove stem and seeds, then chop up and set aside. 

To cook the chicken, place the two chicken breasts in the bottom of a large pot. Season with salt and pepper. Cover the chicken with one inch of water and bring to a gentle boil. Once the water starts to boil, reduce heat and simmer for 10 – 16 minutes (chicken should be 165F in the center when done). Remove chicken breasts and place onto plate or cutting board. Once they are cool enough to handle, use two forks to shred the chicken. 

In a large saucepan over medium heat, heat the heavy whipping cream. Stir frequently until it's reduced by half. Add cooked noodles, shredded chicken, bacon crumbles and chopped poblano pepper. Stir until combined. 

Stir in the cheese and turn the heat down to low. Let cook for 10 – 15 minutes. Gently stir in tomatoes and crushed red pepper flakes.