Place the potatoes in a large pot and add 2 teaspoons salt and enough cold water to cover. Bring to a boil. Reduce heat and simmer until the potatoes are very tender, 20 to 25 minutes. Drain and return the potatoes to the pot.
Add the Cheddar, milk, 1 teaspoon salt, and ¼ teaspoon pepper to the potatoes and mash to the desired consistency. Fold in the chipotles just before serving.