Place chiles on a microwave-safe plate and microwave on high at 15-second intervals until hot, pliable, and toasted-smelling, about 30 seconds total.
Combine all chiles in a medium saucepan and add chicken broth. Simmer over medium-high heat until chiles are completely tender, about 10 minutes. Alternatively, place chiles and chicken broth in a 2-quart microwave-safe container, cover with plastic wrap, and microwave on high power until liquid is simmering, about 5 minutes. Let stand 5 minutes. Transfer to a countertop blender or hand blender cup and blend until completely smooth.
Store chile paste in the refrigerator for up to 1 week. Alternatively, divide paste into ice cube trays, freeze, and transfer frozen chile paste cubes into freezer bags to store in the freezer for up to 6 months.