Peel of the casing of the sausage(s) and discard. Cut the semi-frozen sausage meat into one-inch rings.
Set the stove to high. Heat the olive oil in a skillet (a.k.a. frying pan).
Add the sausage rings, cut side down, in a single layer. Cook without disturbing until the undersides are lightly browned. Flip to brown the other side. The sausage rings won’t crumble once they’re seared and browned.
Add the onion and tomatoes. Cook, stirring occasionally, until the vegetables soften a bit.
Add the basil leaves. Stir.
Push the meat and vegetables around to create three to four craters, depending on how many eggs you want to use.
Crack an egg into each crater. Lower the heat to medium-low, cover and cook until the eggs are set. Sprinkle with chopped parsley and serve the sausages and eggs in the skillet.