Preheat oven to 400°F. Remove the outer papery layers from the bulbs of garlic while keeping it intact. Cut about ¼ - ½” off the top of the heads of garlic, exposing as many individual cloves as possible.
Place the garlic cut-side up on a sheet of aluminum foil. Drizzle with a tablespoon of olive oil. Wrap tightly in aluminum foil and bake for 45 minutes. Cloves should be golden brown and completely soft when pressed.
Remove from oven and allow to cool. Remove the cloves of garlic from the skins, either by squeezing them out or by using the tip of a knife to cut through the skins.
Mash the garlic into a paste with your knife or fork. Make it as smooth as possible to avoid clumps of garlic in your mashed potatoes.
Add cubed potatoes to a large stock pot or Dutch oven and cover entirely with cold water. Heat over medium-high heat until the water reaches a rolling boil. At this point, reduce the heat to a simmer and boil for 20-25 minutes, until potatoes are fork-tender.
Drain potatoes and transfer back to pot or large serving dish. Add roasted garlic paste, vegan butter, and 3/4 cup warm milk. Mash to reach desired texture, adding extra milk if you prefer a thinner consistency. (If you like your mashed potatoes ultra-smooth, invest in a potato ricer!)