Toss the onion, carots, celery, and garlic into the food procesor and process until finely chopped, set aside.
In a large zipper-lock bag or bowl, toss the beef with flour salt, and pepper until evenly coated.
Coat a large nonstick skillet with cooking spray and set it over medium-high heat. When the pan is hot, add the oil, then add half of the beef and brown it onall sides for 3 to 4 minutes. Transger to a large pot. Cook the rest of the beef the same wa and add it to the pot.
Add the chopped onion, carrot, celery, and garlic to the skillet, reduce the heat to medium, and cook for 6 to 7 minutes, or until the vegetables begin to soften. Add them to the pot.
Add the beef broth, tomatoes and their juice, and the broccoli puree, cover, and bring to a boil, then reduce the heat and simmer 4 hours. Add the potatoes and cook until the meat is very tender and begins to fall apart, 4 1/2 to 5 hours total.