Place the potato chunks into a large pot and fill with water. Place over medium-high heat. Let it boil until the potatoes are soft enough to mash, about 10 to 15 minutes of boiling. Turn off the heat and thoroughly drain the potatoes.
Add butter to the pot with the drained potatoes. As the butter melts, mash the potatoes until they are thoroughly mashed and the butter is melted. It’s easiest if you use a potato masher, but not necessary.
Add basil, garlic, milk, salt, and pepper. Mix well. Serve immediately with a drizzle of olive oil on top.