Set a 6-quart Instant Pot to Sauté and melt the butter.
While the butter melts, combine the smoked paprika, garlic powder, onion powder, mustard powder, salt, and pepper in a large bowl or zip-top bag; add the diced chicken and toss or shake to coat evenly.
Add the seasoned chicken to the melted butter and sauté uncovered for about 2 minutes, stirring and flipping frequently.
Add the uncooked penne to the pot, pour the chicken broth over the pasta, and stir to combine, making sure pasta is mostly submerged.
Place the lid on the Instant Pot and seal the vent. Cook at High Pressure for 3 minutes (the pot will take several minutes to come to pressure).
When the cooking time ends, perform a quick release of pressure, then carefully open the lid with protected hands to avoid steam burns.
Return the pot to Sauté, add the cream cheese and push it into the hot pasta so it begins to melt; cover with the lid and let sit for 2 minutes to encourage melting.
Turn the Instant Pot off, open the lid, add the broccoli florets, stir to combine, then replace the lid and let the pot sit, turned off, for 5 minutes so the broccoli steams.
After 5 minutes, open the lid, add the heavy cream, Colby Jack, and Parmesan; stir until cheeses melt and the sauce is smooth. Taste and adjust seasoning as needed.
Garnish with additional Parmesan, crushed red pepper flakes, and fresh basil if desired, then serve.
