Dice the yellow onion into 1/4-inch pieces and set aside. Wash the broccoli and cut into 1-inch florets, discarding the thick stems or reserving them for another use. Melt the butter in a small skillet over medium heat and add the diced onions. Sauté for 3-4 minutes until softened and lightly golden, then remove from heat. This pre-cooking step builds flavor into the soup rather than adding raw onion harshness.

Add the canned cream of celery soup and canned condensed cheddar cheese soup directly to a 6-quart slow cooker. Pour in the evaporated milk and add the broccoli florets. Add the sautéed onions from Step 1 along with the garlic powder, onion powder, ground mustard, paprika, and black pepper. Stir everything together thoroughly to combine all ingredients evenly. I like using evaporated milk here instead of regular milk because it creates a richer, creamier texture without breaking down during the long cooking time.

Cover the slow cooker and set it to LOW. Cook for 3-4 hours until the broccoli is very tender and the flavors have melded together. Stir the soup once at the halfway point (around 1.5-2 hours) to ensure even cooking and prevent any ingredients from settling on the bottom.

After the slow cooker time is complete, stir in the warm cooked rice and the shredded cheddar cheese. Mix well until the cheese is completely melted and incorporated, about 2-3 minutes. The residual heat from the soup will melt the cheese smoothly. Cook on LOW for an additional 20 minutes to allow the rice to warm through and the flavors to fully integrate. I prefer Cabot cheddar because it melts more smoothly into soups without becoming stringy or grainy.