Heat oil in large heavy skillet over medium heat. Sauté onion 5 minutes, until softened; add garlic and cook 1 minute more. Add roasted peppers, tomatoes, and cayenne. Cover and cook 10 minutes, until vegetables are very soft, stirring occasionally. Uncover and simmer over medium heat until sauce is thick, about 10 minutes, stirring often. Season to taste with salt and pepper. (Mixture can be made up to 2 days ahead and reheated).

In large bowl, beat eggs until blended. In large nonstick skillet, melt butter over low heat. Add eggs and basil. Cook, stirring constantly with rubber spatula, 12 minutes, until soft curds form and eggs are barely set. Add pepper mixture and ham; stir just until mixed.