In a large stock pot over medium heat, melt 1 tablespoon butter. Add 2 ribs thinly sliced celery, 2 halved and thinly sliced carrots, and 1 large diced yellow onion to the pot.

Sauté the vegetables for 3 minutes, stirring occasionally, until softened. Add 1 tablespoon minced garlic and cook for another 30 seconds until fragrant.

Add 6 cups beef broth, 8 ounces sliced mushrooms, 2 medium bite-sized Yukon gold potatoes, ½ teaspoon dried thyme, ½ teaspoon garlic powder, 1 teaspoon salt, and 1 tablespoon Worcestershire sauce. Stir to combine.

Bring the broth to a boil over medium-high heat, then reduce heat slightly to maintain a gentle simmer (not a vigorous boil). Cook for 5 minutes.

Add 2 cups dried egg noodles to the pot and stir well to prevent clumping. Continue cooking for 8 minutes, stirring occasionally, until noodles are tender and potatoes are easily pierced with a fork. Reduce heat to low.

Add 1 cup frozen peas and carrots and 2 cups bite-sized leftover prime rib pieces. Stir gently and cook for 2 minutes, just until vegetables are heated through and prime rib is warmed.

Taste and adjust salt if needed. Ladle into bowls and serve immediately.