Soak dried mushrooms in hot water for 15 minutes. Strain mushrooms through a sieve, reserving liquid. While the mushrooms are soaking, cook tortellini according to package directions.
While the tortellini is cooking, heat oil in a large skillet over medium-high heat. Add shallots and garlic and cook 3 minutes, stirring with spoon until soft. Add oregano and bay leaves and cook 1 minute, until fragrant. Add porcini mushrooms and reserved mushroom soaking liquid and bring to a simmer, for 5 minutes. Reduce heat to medium, add heavy cream and simmer 2 minutes to heat through. Remove bay leaves with tongs, add tortellini to the mushrooms and cook 1 minute, to heat through. Remove from heat and stir in cheese and parsley. Serve immediately.