Bring a pot of water to a boil. While that's heating up, cook the chicken thighs in a skillet with 1 tbs of olive oil over medium-high heat for 4 minutes per side. Set aside.
Once boiling, add a big pinch of salt and the penne. Give it a stir. Cook until 1 minute under al dente (so if the box says 11 minutes, cook to 10). Reserve ½ cup of the pasta water then drain the pasta and set aside.
Add a touch more olive oil to the same skillet you cooked the chicken in over medium-low heat. Add the shallots and cook until translucent (about 5 minutes). Add the garlic, red pepper flakes, salt, pepper, and tomato paste. Cook for a few minutes, or until the tomato paste become a deep red.
Add the vodka and cook until ½ reduced. Add the crushed tomatoes, oregano, and fresh basil. Bring to a boil, then reduce to a simmer, partially cover, and cook for 10 minutes. While that's cooking, slice the chicken into small strips or cubes.
Add the heavy cream and stir well to combine. Add the penne and chicken and stir. Cook for 1 minute. Add the Parmigiano. Taste for seasoning and enjoy!