Soak the dried mushrooms in hot water for 15 minutes. Strain them through a sieve while saving the liquid. As the mushrooms are soaking, cook the tortellini following the original package directions.
While the tortellini are cooking, put the oil in a large skillet and heat with medium-high heat while adding the shallots and garlic. Cook them for 3 minutes. Stir with a spoon until they are soft. Add the oregano and bay leaves and cook them for 1 minute until they become fragrant. Add the porcini mushrooms and the saved liquid that the mushrooms soaked in for 5 minutes. Put the heat on medium while adding the heavy cream. Then allow to simmer for 2 minutes in order for the cream to be able to heat up. After it is heated up remove the bay leaves with tongs, add the tortellini to the mushrooms and cook for 1 minute, heating thoroughly. Then remove from the heat and stir in the cheese and parsley and serve right away.