Rinse the beef well under cold water. Transfer to large pot and cover with 4 1/2 quarts of water. Add half the onion, 6 cloves of garlic, Salt, to taste, carrot, celery and 1/3 of the cilantro. Bring up to a boil at medium heat. Reduce heat to below medium. Skim off the foam on top, as needed. Cover 3/4 of the way and continue cooking until beef is tender. This may take more than 2 hours.
Once beef is tender, transfer the beef to a large plate or bowl. Trim away excess fat. Using two forks, shred the beef. Season lightly with salt and pepper, if needed. Cover and set aside.
Strain out all of the solids from the broth left in the pot. Keep warm on low. To the blender jar, add the tomatoes, remaining onion, remaining garlic, serrano, cumin, oregano, pepper, salt, to taste and 1 cup of water. Blend on high until smooth.
Pour blended tomatoes into pot with broth. Turn heat up to medium. When it comes up to a boil, skim some of the excess fat from the top. Taste for salt. Add the bay leaves and 1/2 of the remaining cilantro. Cook for 20 minutes. After 20 minutes, reduce heat to low. Keep covered.
While the soup base simmers, prepare the tortitas: In a skillet, preheat 1 1/2 cups of oil to medium heat for 5 to 6 minutes. In a large bowl, add the egg whites. With an electric hand mixer, beat the egg whites until stiff peaks form, add in the yolks, flour and 1/2 tsp. of salt. Mix on low just until incorporated. Fold in the shredded beef.
Using a large spoon, ladle in about 1/3 cup of the beef/egg mixture into hot oil. Fry 4-5 tortitas at a time for about 4 minutes, turning halfway through cooking times or until golden brown. Drain onto a plate lined with paper towels. Repeat until all the tortitas are done. Yields 15 tortitas.
Warm tortitas(albondigas) for 1-2 minutes in microwave on high. To each bowl, add 3 albondigas. Ladle in enough broth to cover albondigas. Garnish with cilantro, onion, spicy salsa or hot sauce and fresh lime. Serve with or without rice, with warm corn tortillas.