Trim and cut the chicken thighs into approximately 1-inch bite-sized pieces.
Set the pressure cooker to the sauté/brown setting and heat the vegetable oil until shimmering.
Add the chicken to the hot oil and cook, stirring occasionally, for about 3 minutes to brown the pieces; they do not need to be fully cooked.
Add the jarred Alfredo sauce, broth, milk, butter, cream cheese, 1/2 cup Parmesan, salt, pepper, and the penne pasta to the pot; stir to combine and make sure the pasta is submerged in the liquid (add a little more milk or water if needed).
Secure the lid and pressure cook on high for 6 minutes.
Allow a natural pressure release for 5 minutes, then perform a quick release to release remaining pressure; carefully remove the lid.
Stir the pasta and sauce thoroughly until the cream cheese and butter are melted and the sauce is smooth; if the sauce is too thick, stir in a splash of milk or broth.
If using, stir in the frozen peas or other small frozen vegetables until heated through, then taste and adjust seasoning.
Serve hot, optionally topped with fresh grated Parmesan.