1Pour carton of beef broth into at least a 4qt pot/stock pot. Heat to boiling.
2Cut onions into thin slices, then quarter the slices. Add to the broth. Add salt and pepper.
3Bring the mixture back to boiling, then turn the heat down and simmer, uncovered, for 1 hour.
4After simmering for an hour, while stirring, slowly shake the flour in a sifter over the soup. Continue to stir if any large lumps of flour develop. Be careful when you stir; aggressive agitation or using a whisk may tear the onions apart. As the soup continues to cook, any lumps should dissolve.
5After 30 minutes of additional simmering, add the cream and 1 cup cheddar cheese.
Continue to simmer for another 5 or 10 minutes.
6Serve soup hot after sprinkling a tablespoon each of shredded Monterey Jack and Cheddar Cheese on top.