Cook beef in a large nonstick skillet over medium-high heat until browned, stirring to crumble. Add vinegar and 1 teaspoon Italian seasoning. Dollop ricotta cheese, by rounded tablespoons, over meat. Top with broken noodles, making one flat layer (noodles will overlap a little bit).
Pour tomatoes and peppers over noodles, making sure that noodles are completely covered. Add water, and sprinkle with remaining 1 teaspoon Italian seasoning. Dollop pesto by half teaspoons over top. Bring mixture to a boil. Cover, reduce heat, and simmer 30 minutes or until noodles are fully cooked. Uncover and sprinkle with cheese. Cover and let stand 2 minutes or until cheese melts. Cut into wedges. Remove from pan with a slotted spatula.