Step 1Heat oil in nonstick skillet. Add onion and saute over high heat until transparent, 3 minutes. Add tomatoes, reduce heat to medium-low, add sugar, and saute until tomatoes are very soft, stirring occasionally, 10 minutes. Add parsley and salt and pepper to taste. Cool. Transfer to a bowl, cover with plastic wrap, and set aside.
Step 1Melt mozzarella in double boiler set over, but not touching, simmering water. Pour it into large mixing bowl of an electric mixer and beat in 2 eggs. Add 1/4 cup bread crumbs, oregano, half the garlic, and salt and mix well.
Step 2Press cheese mixture into 8-inch square glass dish. Cover and chill until firm, at least 1 hour.
Step 3Lightly beat remaining 4 eggs in bowl. Blend in vermouth. Set aside.
Step 4In a processor or blender, process remaining bread crumbs, Parmesan cheese, parsley, basil and remaining garlic. Set aside.
Step 5Cut cheese mixture into 1 1/2-inch squares (about 15 pieces). Dip each into flour, then egg mixture, and finally into bread crumb mixture to coat evenly. Place on paper towels and refrigerate 30 minutes.
Step 6Heat 3 inches of oil to 375 degrees in heavy skillet or deep fryer. Fry cheese pieces, a few at a time, until evenly golden brown on both sides, 1 minute. Drain on paper towels. Serve at once with Fresh Tomato Sauce.