Heat the cast iron pan over high heat. Roast the sweet peppers for about 15 minutes (5 minutes each side)
Remove the peppers and add the olive oil and the butter to the same pan. Saute the sausages (cut into small pieces) with the garlic.
Toss the butter beans and season them (thyme, black pepper, salt, garlic powder).
Make two holes in the mix and place the eggs in it. Add the roasted peppers (peeled and cut into strings) and cover the skillet with a lid or with aluminum foil. Cook on low heat for 7 - 10 minutes. You can choose if you want a runny or a hard yolk.
Sprinkle with chopped parsley and garnish with arugula.