Bring a large pot of water to a boil with 1 tablespoon salt. Add pasta, and cook according to package directions; drain. Reserve a cup of pasta water for pasta mix as needed.
Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add onion and oregano; sauté 12 minutes or until lightly browned. Add garlic; sauté 2 minutes. Add tomatoes and vinegar; sauté 3 minutes or until tomatoes begin to soften. Add pasta and spinach; cook 1 minute. Remove from heat, and stir in Parmigiano-Reggiano, remaining 1 tablespoon oil, remaining 1/4 teaspoon salt, and pepper. Sprinkle with feta.