Set the Instant Pot to the Sauté function and allow it to heat.
Pat the chicken breasts dry and sprinkle both sides evenly with the Cajun seasoning.
Add the olive oil to the hot Instant Pot and brown the chicken about 3–4 minutes per side; the chicken does not need to be cooked through. Remove the chicken to a plate.
Add the minced garlic to the pot and cook, stirring, for about 30 seconds until fragrant.
Pour in the chicken stock and scrape the bottom of the pot to loosen any browned bits.
Stir in the heavy cream, add the pasta, and sprinkle in the kosher salt. Push the pasta down so it is mostly submerged, avoiding excessive stirring.
Place the browned chicken on top of the pasta mixture. Secure the lid and set the valve to Sealing. Select Manual/Pressure Cook on high for 4 minutes.
When cooking finishes, perform a quick release by moving the valve to Venting (watch for hot steam). When fully depressurized, remove the lid.
Remove the chicken, slice or shred it, and set aside. Stir the thyme, Parmesan, and butter into the pasta until melted and the sauce is creamy.
Serve the pasta topped with the sliced or shredded chicken, diced tomatoes, and minced parsley.
