Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, 20 to 25 minutes.

Meanwhile, melt butter in a small saucepan over medium-low heat. Add garlic and sauté until soft, about 5 minutes.

Drain potatoes and return to the pot. Add garlic-butter mixture, milk, Parmesan cheese, parsley, salt, and pepper; mash until smooth.