Sprinkle beef cubes with S&P, coat lightly with flour, shaking off excess. Brown beef cubes well in heated butter in Dutch oven until lightly browned. When beef is done remove from pan and cook onion is same pan, stirring frequently until soft and lightly browned.
Return beef to pan, mix in garlic, salt, cumin and chili powder. Add tomatoes and their liquid and green chilies. Bring to boiling, cover, reduce heat and simmer until beef is tender. Skim and discard fat.
Mix in beans. Continue cooking, uncovered, stirring occasionally until thickened slightly about 20 minutes.
Sprinkle with cheese. Cook a few minutes longer to melt it.