Add beef roast to slow cooker. Combine remaining broth ingredients and pour over top of roast. Secure lid and cook on low for 6 hours.
In the last 30 minutes of the broth cooking, start water boiling for ramen. Cook ramen as directed on package.
Remove roast from slow cooker and shred. Return shredded beef to slow cooker and secure lid for remainder of cook time.
Start water boiling for eggs. Once boiling, gently add eggs and cook for exactly 7 minutes. Remove eggs to ice bath (half ice half water). Peel shells.
Place a portion of ramen in bowl, along with a portion of scallions. Ladle beef and broth over top of ramen. Split egg in half and add to bowl. Sprinkle with a splash of chili oil.