Lay a boneless and skinless chicken breast on cutting board. With the edge of your knife parallel to the cutting board, begin cutting down the length of the side of the breast. Carefully slice the breast in half lengthwise almost to the other edge. Keep edge intact and open the breast along the fold "like a book". Cover chicken with plastic wrap. Using the flat surface of a meat mallet, gently pound out the chicken until desired thickness is achieved.
Sprinkle each chicken breast front and back with salt, pepper, and paprika.
In a small bowl, mix together cream cheese, pepper jack and cheddar cheese until incorporated well.
Place 1/2 of the mixture onto one side of the chicken breast. Place 1/2 of the jalapenos strips on top of the cheese mixture. Roll chicken starting with the mixture side. Place tooth picks on each side to hold roll together.
Starting at one end of roll, place a piece of bacon on the toothpick end and wrap bacon around chicken roll. You will need 3- 3 1/2 pieces of bacon. to completely cover chicken breast.
Preheat oven to 400 degrees.
Use an oven proof non-stick skillet. Place a drizzle of oil into skillet on medium high. (If you do not have a oven proof skillet, you can use a regular non-stick skillet and transfer the chicken to a baking dish once the bacon is browned completely.)
Place both chicken rolls into pan. Allow bacon to completely crisp and become brown before turning them. Once all bacon on chicken is browned and crisp, place skillet into preheated oven for 25-35 minutes. Check internal temperature of chicken breast before removing from oven. (When checking internal temperature, insert thermometer into thickest part of breast, staying away from the cheesy center.)
Remove chicken from oven and take chicken out of skillet to let rest on a cutting board or a plate. Place skillet on the burner on medium high. Scrape loose any remaining cheese and bacon fat. Add heavy cream, Monterey jack cheese, garlic, salt, pepper, and paprika. Stir for 5 minutes.
Pour sauce onto a serving dish. Cut chicken into thick slices and place onto sauce. Garnish with green onions.
