Cook egg noodles in a large pot of boiling salted water for 6 to 7 minutes until al dente. Drain, toss with 1 teaspoon of melted butter, and set aside.
Heat 1 tablespoon olive oil in a large deep skillet over medium-high heat. Add ground beef, break into crumbles with a spatula, and cook for 5 to 6 minutes until browned and cooked through. Drain excess grease and transfer beef to a plate.
In the same skillet, melt remaining butter over medium heat. Add sliced cremini mushrooms and diced onion. Cook undisturbed for 2 minutes, then stir and sauté for 3 minutes until caramelized and tender.
Add minced garlic and cook for 30 seconds until fragrant. Sprinkle flour over the mushrooms and stir constantly for 1 minute to coat and cook off raw starch.
Gradually pour in beef broth, Worcestershire sauce, Dijon mustard, sea salt, black pepper, and smoked paprika. Stir well, scraping up any browned bits from the pan bottom.
Bring gravy to a gentle simmer for 3 to 4 minutes until thickened and glossy.
Reduce skillet heat to low. Whisk in room-temperature sour cream until smooth and fully incorporated into the velvety sauce.
Return cooked beef and drained egg noodles into the skillet. Toss gently for 1 to 2 minutes until hot and coated in sauce. Garnish with chopped fresh parsley and serve immediately!