Melt 3 tablespoons butter in a large nonstick skillet over medium-high heat. Add the mushrooms, 1/2 teaspoon salt and a few grinds of pepper. Cook until the mushroom liquid evaporates, about 8 minutes. Transfer the mushrooms to a food processor. Add 1 tablespoon Worcestershire sauce, the quinoa, egg, chives, 1/2 teaspoon salt and a few grinds of pepper and pulse until crumbly but not mushy. Wipe out the skillet and reserve.
Preheat the broiler. Line a baking sheet with foil and coat with butter. Use an ice cream scoop to form the mushroom mixture into twenty 1 1/2-inch balls; scoop onto the baking sheet. Broil until well browned, flipping halfway through, about 12 minutes.
Meanwhile, bring a large pot of salted water to a boil. Add the egg noodles and cook as the label directs. Drain well.
Return the skillet to medium-high heat and add the remaining 2 tablespoons butter; let melt. Whisk in the flour until golden brown, about 2 minutes. Whisk in the mushroom broth and heavy cream; cook, whisking, until thick, 2 to 4 minutes. Stir in the remaining 1 tablespoon Worcestershire sauce; season with salt and pepper.
Divide the noodles and meatballs among bowls. Top with the gravy and chives. Serve with lingonberry jam.