Sprinkle beef cubes with salt and pepper; coat lightly with flour, shaking off
excess. Brown beef cubes, about half at a time, well on all sides in heated butter
in a large heavy frying pan or Dutch oven, removing and reserving them as they brown.
When all beef is browned cook onion in same pan, stirring frequently, until soft
and lightly browned.
Return beef to pan; mix in garlic, salt, cumin and chili powder. Add tomatoes,
coarsely chopped, and their liquid, and green chiles. Bring to boiling. Cover, reduce
heat and simmer until beef is tender, 1 1/2 hours. Skim and discard fat.
Mix in beans. Continue cooking, uncovered, stirring occasionally, until thickened
slightly. 20 minutes.
Sprinkle with cheese. Cook for a few minutes longer to melt it.
Serve over rice,
garnishing each portion with avocado slices.