Set Instant Pot to sauté setting and allow it to heat for 1–2 minutes. Add olive oil. Once hot, add chicken pieces and cook for 3–4 minutes, stirring occasionally, until lightly browned (chicken will finish cooking later).
Add garlic powder, onion powder, italian seasoning, salt, and black pepper. Stir to coat the chicken evenly. Pour in a small amount of chicken broth and scrape the bottom of the pot thoroughly to deglaze and prevent a burn notice.
Add the remaining chicken broth, then add uncooked pasta. Gently press the pasta down so it is mostly submerged in liquid. Do not stir excessively.
Place broccoli florets on top of the pasta in an even layer. Do not stir.
Secure the lid and set the valve to sealing. Press the pressure cook button and cook on high pressure for 5 minutes. Note: it will take about 8–12 minutes for the instant pot to come to pressure before the timer begins.
When the timer beeps, carefully perform a quick release by turning the valve to venting. Allow all pressure to release before opening the lid.
Switch back to the saute setting. Stir the pasta and broccoli together. Add heavy cream, cream cheese, and parmesan cheese. Stir until fully melted and a smooth, creamy sauce forms.
Stir in sour cream and let the pasta sit for 2–3 minutes to thicken. Serve warm.