Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil.
Cut green chile peppers in half from top to bottom; remove the stem, seeds, and ribs. Place peppers cut-side down onto the prepared baking sheet.
Cook under the preheated broiler until the skin of the peppers has blackened and blistered, 5 to 8 minutes. Place blackened peppers into a bowl and tightly seal with plastic wrap. Allow peppers to steam as they cool, about 15 minutes. Remove and discard skins. Chop peppers.
Place potatoes and garlic into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until potatoes are fork-tender, about 20 minutes. Drain.
Return potatoes to the pot. Add milk, sour cream, butter, salt, and pepper. Mash with a potato masher until no lumps remain. Stir in the chopped peppers.