Set pressure cooker to saute mode, add the butter and onions. Cook until the onion is softened, about 3 to 5 minutes. Stir in garlic for last minute. Cancel the saute mode.
Add the chicken broth and salt, stir. Then sprinkle rice into the pot, but do not stir.
Place the lid on the electric pressure cooker and set the valve to sealing. Set the pressure cooker to “manual” or “pressure cook” high for 10 minutes. Quick release the pressure when the cook cycle is complete.
Fluff the rice, and then gently stir in the broccoli florets + precooked diced chicken or ham. Place the lid back on and allow the Instant Pot to “keep warm” until the broccoli has softened to your desired tenderness. (typically 10 to 15 minutes)
Once broccoli is tender, stir in the sour cream and 1 ¾ cups cheddar cheese into the rice. Top with remaining cheddar cheese and place the lid over the pressure cooker just until the cheese melts and the remaining water is absorbed. (about 5 minutes)