Make the dough: Mound the 2 cups all-purpose flour on a clean work surface and make a well in the center. Crack in 2 whole 3 eggs 2 whole and 1 yolk, then add the 2 tbsp olive oil and ½ tsp fine salt. Using a fork, beat the 3 eggs 2 whole gently, gradually incorporating 2 cups all-purpose flour from the inner walls of the well. Once a shaggy dough forms, switch to your hands and knead for 8–10 minutes until smooth, elastic, and slightly tacky — it should spring back slowly when poked. If it's too stiff, add 1 tbsp water cold a teaspoon at a time.

Wrap the dough tightly in plastic wrap and let it rest at room temperature for at least 30 minutes. This relaxes the gluten and makes it much easier to roll thin.

Make the filling: In a mixing bowl, combine the ricotta, ½ cup Parmesan cheese freshly grated, ½ cup fresh mozzarella finely diced, 1 yolk, ½ tsp fine salt, ¼ tsp black pepper freshly ground, ¼ tsp nutmeg freshly grated, and 1 tbsp fresh parsley finely chopped (if using). Stir until smooth and well combined. Taste and adjust seasoning. Transfer to a piping bag or Ziploc bag with a corner snipped off. Refrigerate until ready to use.

Roll the dough: Divide the rested dough into 4 equal pieces. Keep unused pieces covered. Using a pasta machine, flatten one piece into a rough rectangle with your hands, then feed it through the widest setting (1). Fold it in thirds like a letter and feed through again. Repeat 2–3 times. Then roll progressively thinner, one setting at a time, down to setting 5 or 6 (about 1–2 mm thick). Alternatively, use a rolling pin to roll as thin as possible on a lightly 2 cups all-purpose flour dusted surface.

Cut hearts: Using a heart-shaped cookie cutter (about 3 inches wide), cut as many hearts as possible from the sheet. Re-roll scraps once to cut more. You'll need an even number of hearts — half for the bottoms, half for the tops. Lay them on a lightly 2 cups all-purpose flour dusted baking sheet and cover with a clean towel to prevent drying.

Fill the ravioli: Lightly brush the edges of half the heart-shaped pieces with 3 eggs 2 whole wash. Pipe or spoon about 1 tsp of filling into the center of each brushed heart, keeping a clear 1/2-inch border around the edges. Don't overfill — this is the most common cause of ravioli bursting.

Seal the ravioli: Place a second heart on top of each filled heart, aligning the edges. Starting from the top center point of the heart, press firmly outward toward the edges, pushing out any air pockets as you go. Press the edges firmly to seal. For extra security, crimp the edges with a fork. Place finished ravioli on a 2 cups all-purpose flour dusted baking sheet in a single layer.

Cook the pasta: Bring a large pot of water cold to a rolling boil and add the 1 tbsp kosher salt for pasta water. Working in 2 batches, gently lower the ravioli into the 1 tbsp water cold. Cook for 3–4 minutes, until the pasta edges are tender and the ravioli float to the surface. Remove with a slotted spoon and set aside. Reserve ½ cup of pasta 1 tbsp water cold before draining.

Make the brown butter sage sauce: While the ravioli cook, melt the 6 tbsp unsalted butter in a large skillet over medium heat. Add the smashed 1 clove garlic lightly smashed clove (if using) and the 8 pieces fresh sage leaves whole. Cook, swirling the pan occasionally, for 3–4 minutes until the 6 tbsp unsalted butter turns golden-brown and smells nutty, and the 8 pieces fresh sage leaves whole turn crispy. Remove the 1 clove garlic lightly smashed. Season with ½ tsp fine salt. If the sauce looks too thick, add a splash of reserved pasta 1 tbsp water cold to loosen it.

Finish and serve: Add the cooked ravioli to the skillet with the brown 6 tbsp unsalted butter sauce. Gently toss or spoon the sauce over the ravioli to coat. Divide among warm plates, spoon any remaining sauce over the top, and finish with freshly grated Parmesan cheese freshly grated and a few pieces fresh sage leaves whole for garnish. Serve immediately.