Add potatoes to stock pot full of water. Cover and boil for 15-20 minutes.
Once potatoes are fork tender drain and leave in strainer.
In the same stock pot melt butter over low heat and add onions and celery. Cook for 8-10 minutes until onions are translucent.
Sprinkle flour over cooked onion and celery. Stir for another minute.
Add vegetable broth, heavy cream, salt, pepper, and Slap Ya Mama seasoning. Stir together and cook until hot.
Add Velveeta and sharp cheddar cheese. Stir until melted.
Mash half of the boiled potatoes and add to soup. Add the remaining potatoes and broccoli florets to the pot.
Continue cooking until the broccoli is tender.