Remove sausage from casing and break up or chop. Cook in a large frying pan set over
medium heat, uncovered and stirring often, until browned. about 10 minutes. Meanwhile,
chop onion. Seed tomatoes and green pepper and coarsely chop. Seed and finely chop
jalapeno peppers.
When sausage is browned, drain off and discard any fat. Stir in onion and cook until
fragrant and just starting to soften. about 1 minute. Stir in tomatoes and peppers. Cook,
uncovered and stirring to bring up any browned bits from pan bottom until hot and
thickened, from 8 to 10 minutes.
When thickened, push mixture aside to make 4 hollows. Break an egg into each space.
Sprinkle eggs with cheese. Cover and continue cooking. In about 5 minutes, egg whites
will be totally set but yolks will still be soft. Serve right away with warm tortillas or thick
slices of toast.