Make the dough: In a small saucepan over high heat, bring the water and 1/4 teaspoon salt to a simmer. Place the flour in a medium bowl. Pour the hot water over the flour and stir with a rubber spatula or wooden spoon to bring it together into a shaggy dough. Pour the mixture onto a lightly floured surface and continue to work and knead the dough for about 5 minutes, or until smooth. Wrap the dough in plastic wrap and allow to rest for at least 10 minutes at room temperature.
Meanwhile, make the filling: In a medium bowl, mix together the ricotta, caciotta, Parmigiano, oregano, egg and salt.
Make the sauce: Heat a saucepan over medium heat. Add the olive oil and garlic and cook for 2 minutes, or until the garlic is lightly browned. Stir in the tomato puree and nestle in the basil sprigs and cheese rind. Season with the salt. Simmer, stirring often, for about 12 minutes, or until the sauce is slightly thickened. Remove and discard the basil and cheese rind.
Bring a large pot of water to a boil. Season with salt. On a lightly floured surface, roll the pasta dough into a large rectangle (6 by 36 inches), about 1/8 inch thick. Place little mounds, about 2 teaspoons each, of the filling about an inch apart down the long edge of the rectangle closest to you. Fold the dough over the filling and gently press around the filling, sealing the dough. Using a small glass or a cookie cutter about 2 1/2 inches round, cut out the ravioli, keeping the folded edge intact. Remove any scrap dough and repeat. You should have about 30 ravioli.
In batches, add the ravioli to the boiling water. Simmer for about 3 minutes, or until they float and are cooked through. Remove with a spider or slotted spoon. To serve, place spoonfuls of sauce in the center of a platter and position the ravioli on top. Sprinkle with grated Parmigiano and garnish with torn basil.