The simple, intense mushroom sauce is also delicious as a chunky topping for toasted slices of country bread.
Place mushrooms in a medium bowl; add 4 cups warm water. Let soak until softened, about 30 minutes. Drain in a sieve lined with a paper towel or coffee filter, reserving liquid. Squeeze mushrooms to remove excess liquid; roughly chop.
Heat butter in an 8- or 10-inch skillet over medium-low heat. Add shallot; cook, stirring occasionally, until softened, about 5 minutes. Raise heat to medium-high; add mushrooms, and cook, stirring often, until golden brown, about 3 minutes.
Add reserved liquid; season with salt and pepper. Bring to a boil. Reduce heat; simmer until sauce is thick enough to coat the back of a spoon, 25 to 30 minutes. Remove from heat; stir in heavy cream.
Meanwhile, cook ravioli in a pot of boiling salted water until they float to the top, according to package instructions. Drain, and divide among serving bowls; spoon mushroom sauce over ravioli.
To prevent the ravioli from sticking while cooking, stir gently after dropping them into the boiling water. To prevent overcooking, remove ravioli with a slotted spoon as soon as they float to the surface of the water.