Traditionally, this chile sauce is made with water, but chicken broth gives it a bit more depth. Look for dried New Mexico chiles in Latin markets, or order from www.chiletoday.com. The sauce may stain some types of pottery and plastic storage containers, so serve and store this in glass containers.
Remove stems and seeds from chiles; discard. Rinse the chiles with cold water; drain. Arrange chiles in a single layer on a baking sheet. Broil 20 seconds on each side or until lightly toasted (be careful not to burn chiles).
Bring 4 quarts water to a boil in a large Dutch oven over medium-high heat. Stir in chiles, and cover. Remove from heat, and let stand 30 minutes or until soft. Drain.
Place half of chiles, 2 1/2 cups broth, and garlic in a blender; process until smooth. Pour the pureed mixture into a large bowl; repeat procedure with remaining chiles and broth. Strain chile mixture through a sieve into a large saucepan, and discard solids. Stir in salt. Cook over medium heat 30 minutes, stirring occasionally.