Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Once the oil is shimmering, place the beef chuck roast in the pan and sear it on all sides. Allow each side to develop a deep brown crust before turning, which should take approximately 2 minutes per side. This step enhances the depth of flavor in the broth.

Transfer the seared beef chuck roast to a large stockpot and add 8 cups of water, ensuring the beef is fully submerged. Bring the water to a boil, then reduce to a gentle simmer.

Using a fine mesh strainer or spoon, remove any foam or impurities that rise to the surface to achieve a clearer broth. Allow the beef to simmer for approximately 3 hours, or until it becomes tender and easily pulls apart. Add additional water during cooking if necessary to maintain the broth level.

Once the beef is tender, remove it from the broth and let it rest on a cutting board before slicing it into bite-sized pieces. Set aside.

While the beef is simmering, prepare the hard-boiled eggs. Place the eggs in a saucepan and cover them with water. Bring the water to a boil, then immediately remove the saucepan from heat and cover it with a lid. Let the eggs sit in the hot water for 15 minutes before transferring them to an ice bath. Once cooled, peel the eggs and slice them in half. Set aside.

Once the beef is fully cooked and removed from the pot, cook the spaghetti according to the package instructions. Drain and set aside until ready to assemble the dish.

Measure out 8 cups of the beef broth, ensuring enough remains for all servings. If necessary, add additional water to reach this amount.

Stir well and allow the broth to simmer for 3 additional minutes to incorporate the flavors fully. Taste and adjust seasonings as needed.

Return the sliced beef to the broth and let it warm through.

For each serving, divide the cooked spaghetti among four bowls. Ladle 2 cups of the seasoned broth into each bowl, ensuring an even distribution of liquid and beef.

Serve immediately while hot.