Set an Instant Pot to sauté on high. While it heats, cut the chicken into 1/2-inch pieces. When the pot registers hot, add the butter, stirring to melt. Stir in the paprika and mustard powder and cook until lightly toasted, about 30 seconds. Add the chicken and a pinch each of salt and pepper and stir to coat, then turn off the pot.
Add the pasta, chicken broth and 1 cup hot water to the Instant Pot. Put on and lock the lid; make sure the steam valve is in the sealing position. Set the pot to pressure-cook on high for 3 minutes. When the time is up, carefully turn the steam valve to the venting position to manually release the pressure. Turn off the pot and remove the lid.
Set the Instant Pot to sauté on high. Bring the liquid to a boil, stirring well. Add the heavy cream and parmesan and cook, stirring, until the sauce thickens, 2 to 3 minutes. Turn off the pot, add the broccoli and cheddar and stir until the broccoli is bright green and the cheddar melts, 2 to 3 minutes. Season with salt and pepper.