With a sharp knife, slice the top off of each of the bulbs of garlic. Drizzle the open end of each with approximately 1 teaspoon olive oil, and wrap it in foil. Bake in a 400° F (204° C) oven for half an hour or until soft. (I use my toaster oven for this.)
Meanwhile, scrub or peel the potatoes. (I don't peel new potatoes.) Cut them into approximately 1-inch (2.5 cm) chunks. Boil the potatoes in water until soft, or follow Instant Pot instructions.
Instant Pot Instructions: Add potato chunks and one cup of water to the Instant Pot. Cook at high pressure for 3 minutes. Allow pressure to release naturally for 6 minutes. Release remaining pressure. Drain the potatoes.
Measure out the dairy free milk, olive oil, salt, and pepper into a liquid measuring cup. Once the garlic is cooked and cool enough to handle, squeeze the soft cloves out of their skin and into this liquid. If you don't have a stand mixer, blend this liquid with an immersion blender or in an upright blender. Then mash this mixture into your cooked, drained potatoes with a potato masher.
Stand Mixer Instructions: If you have a stand mixer, you can simply add the drained, cooked potatoes, roasted garlic cloves, and all of the other ingredients to the bowl of a stand mixer. Process it all with the medium paddle until your mashed potatoes look smooth and creamy.
Serve mashed potatoes warm. You can keep them warm in a slow cooker (or the slow cook setting on your Instant Pot) until you are ready for them.
If you'd like to make them a day or two ahead, keep them in the refrigerator. A few hours before serving, heat them up and keep them warm in a slow cooker.
The leftovers are really good fried in a generous splash of olive oil in a hot cast iron pan!