Cook the pasta (1/2 of a 1 lb box) according to package directions. SET ASIDE ONE CUP OF PASTA WATER BEFORE draining the pasta when cooked.
Finely chop one red bell pepper and 1/2 of a medium yellow onion. Set aside.
Heat 1 tbsp of olive oil in a large skillet over medium-high heat.
Lightly salt both sides of the boneless chicken breasts.
Carefully add the chicken to the skillet and cook turning occasionally until golden brown on both sides and cook through, about 7 minutes.
Remove the chicken to a plate and set aside.
If the skillet is dry, add the additional tbsp of olive oil.
Sauté the onions and peppers together over medium-high heat until they are soft and the onions translucent, about 5 minutes.
Create your roux. Add 3 tbsp of butter to the skillet with the vegetables.
Sprinkle the 3 tbsp of all purpose flour over the melted butter and veggies, stirring constantly.
When the flour is fully incorporated, add the heavy cream to the skillet in a steady stream. Stir continually, lowering the heat to medium.
Slowly add in the chicken broth and stir to combine.
Sprinkle the cheese over the ingredients in the skillet and stir continually until it is completely melted.
Add the smoked paprika and a pinch of crushed red pepper flakes and stir.
Reduce the temperature to low.
Cut the chicken into small pieces and add to the cheese sauce. Stir to combine.
Add the drained, cooked spaghetti to the chicken and cheese sauce.
Gently toss to coat the spaghetti in the sauce.
Add pasta water, a little bit at a time, until the sauce has the desired thickness/texture. Stir after each addition.
Salt to taste.