Heat olive oil in a big skillet over medium heat. Add shallots and cook 3–4 minutes until soft and translucent.
Add minced garlic and cook for 1–2 minutes more. Add tomato paste and stir 2 minutes to combine.
Add crushed tomatoes and red pepper flakes. Simmer for 10 minutes, stirring occasionally.
Season chicken breasts and cook in a separate skillet over medium-high heat, 6–8 min per side. Rest and slice into strips.
Reduce tomato sauce heat to low. Pour in vodka, cook 2–3 minutes to evaporate alcohol. Stir in heavy cream until smooth.
Add sliced chicken into sauce. Stir and cook 5 minutes to heat through.
Cook penne pasta to al dente per package instructions.
Drain pasta and plate. Spoon chicken vodka sauce over top.
Garnish with chopped fresh basil and optional parmesan or parsley.
Serve immediately while hot.
Notes
You can quick release pressure for pasta or slow release for more flavor. Add parmesan for extra richness. Leftovers are amazing, just reheat with a splash of broth.