1. To prepare pasta, lightly spoon flours into dry measuring cups; level with a knife. Combine flours and 1/4 teaspoon salt in a food processor; process 30 seconds. Combine 5 tablespoons water, 2 tablespoons olive oil, and eggs in a bowl, stirring well with a whisk. With processor running, pour water mixture through the food chute, processing just until dough forms a ball. Turn dough out onto a lightly floured surface; knead 5 or 6 times. Shape dough into a disk. Dust dough lightly with flour; wrap in plastic wrap. Let stand 30 minutes.
2. Divide dough into 3 equal portions. Working with 1 portion at a time (cover remaining dough to prevent drying), press dough into a flat rectangle. Roll the dough into a 14 x 14–inch square, dusting with flour, if necessary (turning dough over occasionally and dusting surface with flour as needed). Lay dough sheet flat; fold ends so they meet in the middle. Fold the sheet in half like closing a book. Fold in half again to form 8 layers of pasta. Using a sharp knife, cut the pasta crosswise into 1/4-inch-wide noodles. Separate noodles, and dust with flour. Place noodles on a jelly-roll pan dusted with flour. Repeat procedure with remaining dough portions.
3. Bring 6 quarts water and remaining 1 tablespoon salt to a boil in a large Dutch oven. Place noodles in a sieve; shake off excess flour. Add noodles to pan. Cook 1 1/2 minutes or until done; drain.
4. To prepare sauce, heat 2 tablespoons oil in a large nonstick skillet over medium-low heat. Add garlic to pan; cook 3 minutes, stirring frequently (do not brown). Remove from heat. Stir in tomatoes and remaining ingredients. Toss with noodles.