Bring a large pot of salted water to a boil. Add the tortellini and cook as the label directs. Reserve 1/4 cup cooking water, then drain.
Meanwhile, melt the butter in a large skillet over medium heat. Add the mushrooms and shallots and cook, stirring occasionally, until softened, 4 to 5 minutes. Increase the heat to medium high and cook until the mushrooms start browning, 1 to 2 minutes. Sprinkle with the paprika, thyme, 1/4 teaspoon salt and a few grinds of pepper.
Push the mushrooms to the edge of the skillet and add the tomato paste to the center; cook, stirring, until slightly darkened, about 1 minute. Stir the tomato paste into the mushrooms, then stir in the beef broth and heavy cream. Simmer until slightly thickened, about 2 minutes.
Add the tortellini to the sauce and toss, adding the reserved cooking water as needed to loosen. Top with parsley.