Cheese-Filled Toasted Ravioli

For the Pasta Dough: In a food processor, pulse flour with salt and semolina until combined, about 3 pulses. Add the eggs and yolks and pulse until incorporated, about 7 pulses. With the machine on, add olive oil in a thin stream and process until mixture forms a cohesive dough, about 4 pulses. Serious Eats / Robby Lozano Turn out dough onto a semolina-dusted work surface and knead until smooth, about 10 minutes. (The dough should have the consistency of modeling clay and bounce back when poked.) Wrap dough tightly in plastic wrap and let rest at room temperature for 30 minutes or up to 4 hours. Serious Eats / Robby Lozano For the Cheese Filling: In a medium bowl, stir together ricotta, mozzarella, and salt until combined. Cover and refrigerate until ready to use. Serious Eats / Robby Lozano To Roll the Pasta: When dough is done resting, cut into 4 equal pieces and loosely cover with plastic wrap on a semolina-dusted surface. Working with 1 piece at a time (and keeping remaining pieces covered), flatten dough into a 5- by 4-inch oval, about 1/4 inch thick. Dust both sides lightly with semolina flour. Serious Eats / Robby Lozano Using a pasta machine with rollers set to widest setting, feed dough through rollers twice. Bring tapered end of dough toward middle to press to seal, folding in thirds like a letter. Feed dough, seem side first, through rollers again at the same setting. Repeat folding and rolling once more, lightly dusting dough with semolina before each roll. Dough should be smooth and rectangular in shape. (Using a stiff pastry brush, clean the pasta machine of any excess dough or semolina between rolling.) Serious Eats / Robby Lozano Narrow rollers to next setting and feed dough through rollers twice more. Continue to progressively narrow rollers, feeding dough through each setting twice, until you reach the lowest setting and the dough is very thin and semi-transparent (you should be able to see the outline of your hand through it.) Serious Eats / Robby Lozano Transfer dough sheet to liberally floured work surface. Halve the dough sheet crosswise. On one cut dough sheet, spoon 8 mounded tablespoonfuls of filling in 2 rows of 4, spaced 1 inch apart and leaving 1 inch from edges of dough. Top with the second dough sheet. Use your fingers to press dough layers together around the mounds of filling while pressing out any air. Serious Eats / Robby Lozano Using a fluted pastry cutter or a sharp knife, cut between the mounds to form squares, about 2 1/2- by 2 1/4-inches each. (You should have about a 1/2-inch dough border around each mound of filling.) Serious Eats / Robby Lozano Transfer cut ravioli to a rimmed baking sheet liberally dusted with semolina. Repeat with the remaining pasta dough and filling. Freeze ravioli on the semolina-dusted baking sheet until hard, about 30 minutes. Serious Eats / Robby Lozano For the Ravioli: In a medium bowl, whisk eggs and milk. In a shallow dish or pie plate, combine breadcrumbs, parsley, rosemary, thyme, salt, and pepper. Serious Eats / Robby Lozano Working one at a time, dip ravioli into egg mixture, letting excess drip off, then dredge in breadcrumb mixture, pressing to adhere. Return to baking sheet and freeze until hard, about 15 minutes. Set a wire rack inside a rimmed baking sheet and line rack with a double layer of paper towels. Serious Eats / Robby Lozano In a Dutch oven, heat about 1 inch of vegetable oil until a thermometer registers between 335°F and 350°F (168ºC and 177ºC). Fry the ravioli in batches of 4, turning as needed with a slotted spoon, until golden brown all over, about 2 minutes per batch. Transfer fried ravioli to the prepared cooling rack and immediately sprinkle with some of the Parmesan. Serious Eats / Robby Lozano Serve hot with marinara sauce for dipping. Serious Eats / Robby Lozano