Preheat oven to 250°. Core the tomatoes and cut in half lengthwise, and arrange cut side up in a 9"x13" baking pan. Drizzle with the olive oil, scatter the sliced garlic evenly over the top of the tomatoes, and sprinkle with salt, pepper and oregano. Bake for 2–3 hours or until tomatoes are very soft.
On a working surface, pour out the flour into a mound. Make a well in the middle and break the eggs into the well. Using a fork, beat the eggs lightly. Start to incorporate the flour into the eggs while beating. When it becomes difficult to beat, sweep the flour over the egg mixture and with your hands start to mix and knead in the remaining flour. Knead the dough for about 10 minutes or until smooth, adding flour as needed.
On a floured surface, let the dough rest for 30 minutes under an overturned bowl. Cut the ball of dough into 2 pieces. Keep one ball under the bowl. Lightly flour the work surface. Flatten out the ball to a disk shape. Starting at the middle of the disk, roll the dough out and away from you. Give the dough a 1/4 turn and repeat. Continue rolling and turning until the dough is very thin and almost transparent. Put this pasta sheet aside and roll out the remaining dough. Dust the pasta sheets with a little flour and let sit for 20 minutes. Roll the pasta sheet into a loose cylinder about 3 inches wide. With a sharp knife, cut the dough into ribbons 3/4" wide. Unfurl the ribbons and let dry at least 10 minutes before cooking.
When the tomatoes are roasted, cut into pieces with scissors and transfer (with juices) to a large mixing bowl. Add the olives, basil and parsley to the bowl. Set aside.
Bring a large pot of water to a boil. Add 2 teaspoons salt to the water, add the pasta ribbons and stir. Cooking time should be 3–4 minutes, but will depend on the dryness of the pasta, so taste frequently. Scoop out and set aside some of the boiling water, then drain the pasta and transfer it to the tomato mixture. Toss well, adding the reserved pasta water as needed.