Squeeze the thawed broccoli hard. Press it between paper towels or wring it in a clean kitchen towel until no more water comes out. Wet broccoli is the number one reason this casserole turns soupy.
Use uncooked instant rice, not regular long-grain and not pre-cooked rice. Instant rice is the intended ingredient here, and it hydrates in the casserole's own liquid while baking.
Velveeta and Cheez Whiz both work. Velveeta gives a slightly firmer set, Cheez Whiz a looser, glossier sauce.
Swap the cream of mushroom for condensed cream of chicken or condensed cheddar cheese soup if that is what your family makes.
Serve it alongside roast turkey at Thanksgiving or a glazed ham at Easter. It also holds its own next to cornbread dressing and sweet potatoes on a potluck table.
Assemble up to a day ahead, refrigerate unbaked without the cracker topping, then add the crackers and add 10 minutes to the bake time.
Leftovers keep 4 days covered in the fridge. Reheat covered at 325 F so the rice does not dry out, uncovering at the end to re-crisp the top.