Place chiles on an aluminum foil-lined baking sheet. Broil chiles 3 inches from heat 8 to 10 minutes on each side or until charred. Place chiles in a heavy-duty, zip-top plastic bag; seal and let stand 10 minutes to loosen skins. Peel and seed chiles, discarding skins.
Combine chiles and broth in a blender or food processor; process until smooth.
Melt butter in a large skillet over medium heat, and stir in chile mixture. Add cream cheese and cheddar cheese, stirring constantly. Cook 2 to 3 minutes, stirring constantly, until cheeses melt.