Combine the ingredients in a food processor. Process until the dough mixture leaves the sides of the bowl. Remove to a mixing bowl and knead by hand for a few minutes until smooth. (If the dough is too dry, add a few drops of water.) Divide into 4 equal parts and shape them into discs. Wrap in plastic wrap and let rest for 1 hour.
Put the cheeses, salt, and pepper in a blender and pulse. Add the egg yolks and pulse until incorporated.
Roll the discs of dough into thin sheets in a pasta machine. Arrange tablespoon-size dollops of the filling 1 1/2 inches apart on one of the sheets. Brush a little egg white around each dollop, then place another sheet directly on top. Gently press around the filling to remove any air pockets and seal the sheets. Using a ravioli cutter or a knife, cut out ravioli squares. Sprinkle with flour to prevent the dough from sticking.
Cook the ravioli in plenty of boiling salted water until they float to the top, 3 to 4 minutes. Drain well and toss with the Fresh tomato sauce . Garnish with the remaining chopped basil and serve immediately.
