Heat the EVOO, 3 turns of the pan, in a medium pot over medium-high heat. Add the potatoes, onion and garlic as you chop them; season with the rosemary, salt and pepper and cook, stirring frequently, until the vegetables soften a bit, 7 to 8 minutes. Add the cauliflower and cook for a few minutes. Stir in the peppers and chicken broth, cover and bring to a boil. Add the kale to the pot by the handful, letting each handful wilt before adding the next. Season with the nutmeg and cook for 5 minutes, then adjust the salt and pepper.
Ladle the stoup into bowls and sprinkle with the grated Pecorino Romano at the table. Pass around the crusty onion-roll sticks for dunking.