Add onion, garlic, rice, chicken broth, salt, and cooked chicken into the bottom of your Instant Pot.
Seal lid and turn valve to SEALING. Set MANUAL and set timer to 7 minutes.
Once time is up, turn the knob to VENTING to let the pressure out (a quick release).
While the pressure is being released, steam your broccoli in the microwave for 4-5 minutes or on the stove top (or follow directions on the frozen broccoli package if using frozen).
Stir in the broccoli and cheddar cheese.
Add salt and pepper to taste.
Dish onto plates or bowls and top with more shredded cheese, if desired.
Notes
You can cook your fresh broccoli in with the other ingredients, but it will kind of disintegrate/fall apart for cooking that long in the Instant Pot. If your kids don't love broccoli, this might be a great option! But if you like broccoli and prefer the bigger pieces, follow the instructions as written.