In a large mixing bowl, combine the flour and salt. Make a well in the center and add the eggs and olive oil. Using a fork, gradually combine the flour with the eggs until a dough starts to form.
Transfer the dough to a lightly floured surface and knead for about 5-7 minutes until smooth and elastic. Wrap in plastic wrap and let it rest for at least 30 minutes.
In a skillet over medium heat, add a splash of olive oil. Once hot, add garlic and sauté for 1 minute until fragrant. Add the chopped mushrooms and thyme, cooking until the mushrooms are tender and any liquid has evaporated (about 5-7 minutes). Allow to cool slightly.
In a bowl, mix the sautéed mushrooms with ricotta cheese and Parmesan. Season with salt and pepper to taste.
Divide the rested dough into four pieces. Roll out each piece into thin sheets using a pasta machine or a rolling pin until about 1/16-inch thick.
On one sheet of pasta, spoon small dollops of the filling about 2 inches apart. Using a brush or your finger, moisten the edges around each spoonful with a bit of water. Carefully place another sheet of pasta on top, sealing around each filling with your fingers to remove any air and ensure they are well sealed. Cut into squares or circles using a pasta cutter.
Bring a large pot of salted water to a gentle boil. Add the ravioli in batches and cook for 4-5 minutes or until they float to the top. Use a slotted spoon to remove them and drain excess water.
In the same skillet used for the mushrooms, pour in the heavy cream and bring to a simmer. Stir frequently until it thickens slightly. Mix in any remaining mushrooms and adjust seasoning with salt and pepper.
Gently add the cooked ravioli to the cream sauce, tossing carefully to coat.
Notes
Serve in shallow bowls with extra cream sauce and garnish with fresh parsley and Parmesan cheese.