Chop potatoes to evenly sized chunks. Bring to a boil in a large pot of salted water; cook for 10 to 15 minutes (depending on the size of the chunks) until potatoes easily split apart when poked with a fork.

Drain potatoes, then return to pot and set over low heat. Mash potatoes with a potato masher on the heat for 1 to 2 minutes (doing so will allow the excess moisture to evaporate). Remove from heat and continue mashing until mostly smooth.

Add olive oil and mash to incorporate, then add milk, salt, and pepper and mash until smooth and creamy. Optionally add 2-4 additional tablespoons of milk to achieve desired consistency.

Transfer to a serving bowl. Drizzle with olive oil and sprinkle with smoked paprika, if desired. Serve warm.