Put potatoes in a large pot and add enough cold water to barely cover. Stir in 1 tsp. salt. Bring to a boil over high heat, covered. Reduce heat to medium and boil gently until potatoes are tender when pierced, about 15 minutes. Drain; return to pot, off the heat.
Mash hot potatoes with a potato masher until all large chunks are broken and potatoes are fluffy. Add milk, 2 tbsp. butter, and 1 1/2 tsp. salt; mash to blend. Top with remaining 1 tbsp. butter.
Make ahead: Up to 1 day, chilled. Reheat in a microwave until hot (if they've stiffened up, add enough milk to make them creamy).
Mashed Potatoes with Herbed Greek Yogurt: Combine 1 cup whole-milk Greek yogurt with 1 cup of your favorite chopped herbs (we like parsley, dill, and chives). Mix into finished Creamy Chunky Mashed Potatoes. Scatter an additional 2 tbsp. herbs on top.
Mashed Potatoes with Roasted Cauliflower: Put oven rack in top third of oven and preheat to 450°. Place 12 cups cauliflower florets, cut no larger than 1 in., on a rimmed baking sheet. Toss with 2 tbsp. extra-virgin olive oil and 1/2 tsp. each kosher salt and pepper to coat evenly. Spread in a single layer and roast until cauliflower is very tender and brown on the edges, turning occasionally, about 25 minutes. Set aside about 1/3 cup of the best-looking florets, then coarsely mash remaining florets on baking sheet with a potato masher. In step 2, mix mashed florets and 1/2 cup warmed milk (not 1 cup as in the basic recipe) into mashed potatoes. Add 2 tbsp. unsalted butter, 1 1/2 tsp. salt, and pepper to taste. Top with reserved cauliflower and 1 tbsp. butter. Make ahead: Cauliflower, up to 3 days, chilled; reheat before using.