1Steam potatoes, covered, adding more boiling water as needed, until tender. Let cool, then peel and thinly slice.
Heat oven broiler. Heat oil in an ovenproof 12" nonstick skillet over medium-high heat. Cook garlic, pepper, and onion until soft, 3–4 minutes. Add spinach; cook until wilted, about 1 minute. Stir in potatoes, butter, salt, and pepper. Stir in half the basil and the eggs and reduce heat to medium; cook until golden on the bottom, 8–10 minutes. Broil until set and golden on top, about 3 minutes. Garnish with remaining basil.