Add peeled and cubed potatoes to a large stockpot and cover with water, making sure the water reaches at least 1 inch above the potatoes. Heat over medium-high heat and boil until the potatoes are tender and break apart easily with a fork, about 15-20 minutes once boiling.

Drain the potatoes well so excess cooking water does not make the mashed potatoes watery. Mash with a potato masher.

Add 4 tablespoons butter, 1/2 cup milk, 1/2 teaspoon salt, and 1/4 teaspoon ground black pepper. Mix until creamy. Add additional milk a little at a time, up to 3/4 cup total, only if needed for your preferred mashed potato consistency.

Spread half of the mashed potatoes into a serving dish. Spoon small dollops of pumpkin mixture over the potatoes and gently swirl them together with a spoon.

Add the remaining mashed potatoes and pumpkin mixture. Swirl again, leaving some orange pumpkin and white mashed potatoes visible rather than completely mixing them together.

Drizzle the top with olive oil and sprinkle with coarsely ground black pepper. Add chopped fresh chives, if desired, and serve immediately.