Prick sausage casings with a fork. Add 1/2 inch water, a drizzle of EVOO and the sausages to a cast-iron skillet. Bring water to a boil and cook sausages through over medium-high heat until water evaporates. Cook to crisp casings and remove.
Add more oil to pan, 2 turns of the pan, along with fennel, onions and peppers. Cook to tender-crisp, 8-10 minutes, then add garlic, reduce heat a bit and add chili flakes, oregano, vinegar and a splash of water. Bring to a bubble. Slice sausages on bias and add to pan; toss with basil.
In a small, nonstick skillet, cook 1 or 2 eggs at a time, covered, over medium heat to desired doneness. Place eggs over the sausages and veggies and serve directly from the skillet with bread alongside for mopping.
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