FILLING: In 10-inch skillet over medium-high heat, cook beef, onion, and garlic until all pan juices evaporate, onion is tender, and meat is browned. Remove skillet from heat; stir in parsley, cheese, and 1/2 ts salt, then egg. Cover and refrigerate ground beef filling.
RAVIOLI DOUGH: In large bowl, stir 2-1/4 cups flour with remaining ingredients to make a stiff dough. On well-floured surface, knead dough until smooth and not sticky, about 20 times. Cover dough with plastic wrap and let rest 30 minutes for easier rolling.
Cut dough into 4 pieces. On floured surface with floured rolling pin, roll 1 piece into 12 by 8 rectangle. With dull edge of knife, lightly mark dough into twenty four 2-inch squares. Place a scant teaspoon of ground beef filling in center of each square.
Roll second piece of dough into 12 by 8 rectangle; place over filling. Press around filling and along edges. With cutter or knife, cut into 24 ravioli; place in single layer on floured, clean cloth towel. Repeat with remaining dough and filling. Let ravioli dry 30 minutes.
In 8 quart saucepan over high heat, heat 6 quarts water and 2 teaspoons salt to boiling. Add ravioli, stirring gently to separate pieces so they do not stick together; heat to boiling. Reduce heat to medium; cook until tender but firm. About 5 minutes. Drain ravioli; serve with sauce.
MARINARA SAUCE: In 2 quart saucepan over medium-low heat, in hot oil, cook onion and garlic until tender. Stir in sugar, basil, salt, tomatoes with their liquid, and tomato paste; heat mixture to boiling, stirring to break up tomatoes. Reduce heat to low; cover saucepan and simmer 20 minutes to blend flavors, stirring occasionally.