Heat the olive oil in a large pot over medium heat and add the garlic and chicken. Fry the chicken until it turns brown, but is not completely cooked inside.
Stir in the roasted red bell peppers and hot peppers and fry for 1 min. Add the Cubetti and white wine. Add the water and the pasta and bring gently to a boil. (If there is not enough liquid, add some more water.) Continue cooking while stirring regularly until the pasta is cooked al dente. This takes approx. 15-20 min.
Reduce the heat and add basil and salt. When the butter is completely melted in the pasta, add the cream and cheese. Let it simmer for another 10 minutes, while stirring occasionally. Sprinkle some extra cheese and basil and garnish with chili flakes if you really want it hot!