Discard fat from 1 can (49 oz.) chicken broth. Combine broth and 1 1/2 cups tomato salsa in a 5- to 6-quart pan. Cover and bring to a boil over high heat, then reduce heat to just below an active boil. Crack 8 large eggs, one at a time; hold each close to soup surface and slip egg into pan. Cover and cook until yolks are as firm as you like, 4 to 5 minutes for slightly soft centers. Ladle 2 eggs into each bowl; fill bowls with soup. Sprinkle 1 cup shredded cheddar cheese equally over portions.