Put the potatoes in a large pot and cover with 2 inches of water; stir in 1 tablespoon of salt. Bring to a boil over medium-high heat, then reduce the heat slightly and simmer until tender, about 12 minutes.
While the potatoes are cooking, combine the parsley, olive oil, chives, oregano, garlic and 1/4 teaspoon salt in a blender and puree until almost smooth. If it needs more liquid, add a little water, 1 tablespoon at a time, until the mixture blends easily.
Drain the potatoes and return to the pot. Pour in the warm milk and melted butter and coarsely mash with a potato masher. Transfer the mashed potatoes to a serving bowl and top with the herb oil.