In a large mixing bowl, combine the all-purpose flour and a pinch of salt. Create a well in the center.

Crack the eggs into the well and add the olive oil.

Using a fork, gradually incorporate the flour into the wet ingredients until a dough forms.

Knead the dough on a lightly floured surface for about 5-7 minutes, or until smooth and elastic.

Wrap the dough in plastic wrap and let it rest at room temperature for at least 30 minutes.

In a separate mixing bowl, combine the finely chopped white kimchi, ricotta cheese, grated Parmesan cheese, minced garlic, salt, pepper, and one egg. Mix until well combined.

Roll out the rested dough on a floured surface to your desired thickness.

Spoon small portions of the white kimchi filling onto one half of the rolled-out dough, leaving space between each spoonful.

Fold the other half of the dough over the filling.

Press down around each mound of filling to seal the ravioli.

Use a knife or a ravioli cutter to cut out individual ravioli squares or circles.

In a skillet, sauté the chopped shitake mushroom and chopped onion in butter until fragrant.

Add ground nutmeg and stir for about a minute.

Pour in the milk, half and half, and pasta cooking water. Let the mixture simmer for a few minutes until slightly thickened.

Stir in the grated Parmesan cheese until melted and smooth.

Season the sauce with salt, black pepper, and adjust seasoning to taste.

Bring a large pot of salted water to a boil.

Carefully add the ravioli to the boiling water and cook for about 3-4 minutes, or until they float to the surface and are tender.

Using a slotted spoon, remove the cooked ravioli from the water and transfer them to serving plates.

Spoon the prepared sauce over the cooked ravioli.

Garnish with additional grated Parmesan cheese and chopped parsley, if desired.

Serve hot and enjoy your homemade White Kimchi Ravioli!