Place into a large bowl and sprinkle with flour, mixing well to coat.
In a large frying pan, heat olive oil on medium high heat.
Add coated meat cubes and fry until lightly browned, about 5 minutes, stirring frequently.
Transfer meat cubes to a large cooking pot.
Add chopped garlic, chopped onions, red kidney beans including liquid, plum tomatoes including liquid, tomato paste, beef broth, mushrooms including liquid, chili powder, ground cumin, sugar, Italian seasoning, cayenne pepper, dried oregano leaves, black pepper, salt, sweet red pepper, green pepper and celery and simmer covered, for at least 1 1/2 hours, stirring occasionally.
Add beer and red wine and continue to simmer covered, for 15 minutes.
At this time, adjust seasonings to taste.
In a small bowl, mix together tapioca starch with 1/4 cup of water.
While chili is simmering add tapioca mixture to thicken slightly.
When serving, add some grated sharp cheddar cheese and finely chopped onions for garnish.
You can substitute and use 2 pounds of lean ground round instead of chuck steaks.
Dredge ground round in flour and fry until lightly browned.