Combine the ricotta, Parmesan, goat cheese, sage, garlic, and lemon juice in a small bowl.

Add the egg yolk and stir until smooth. Transfer the filling to a piping bag or zip-top bag with one corner cut off. Refrigerate until ready to use.

Add the all-purpose flour, semolina flour, and kosher salt to a food processor and pulse to combine.

Add the egg yolks and olive oil and pulse to combine.

With the food processor running on low, add the cold water and pulse until the dough forms a loose ball.

Turn the dough onto a clean surface and knead for about 30 seconds, just until it forms a smooth ball.

Wrap the dough tightly and let it rest at room temperature for 30 minutes. Make the filling while the dough rests.

Dust the work surface with semolina and divide the dough in half. Keep one half tightly covered while you roll the first piece.

With a KitchenAid pasta attachment, begin at setting #1 and pass the dough through the rollers, moving down one setting at a time until you reach setting #5. Dust with semolina as needed. Or, use a rolling pin to roll the dough evenly until it is thin enough to see your fingers through it.

Trim the rolled dough into 2 equal rectangles.

Pipe small mounds of filling onto one rectangle, leaving enough space between them to cut the ravioli.

Place the second sheet of dough on top. Press out the air around each mound of filling, then seal the dough firmly around the edges.

Cut the ravioli and arrange them in a single layer on a semolina-dusted baking sheet.

Repeat the rolling, filling, and cutting process with the remaining dough.

Let the ravioli dry at room temperature for 30 minutes.

Bring a large pot of salted water to a boil. Cook the fresh ravioli until they float, about 2 minutes. Reserve ¼ cup pasta water, then transfer the ravioli with a slotted spoon.

Meanwhile, melt the butter in a skillet over medium heat and cook until it is browned and smells nutty. Add the sage leaves, remove the skillet from the heat, and stir in the reserved pasta water.

Add the cooked ravioli to the sage brown butter and toss gently. Season the sauce with salt and pepper to taste. The complete cooking phase takes about 5 minutes.