Add your quartered potatoes and whole garlic cloves to a medium pot. Fill the pot with water so that all the potatoes and garlic are covered.
Place your pot on the stovetop and turn the heat to high. Allow to cook until water comes to a boil. Reduce the temp to medium/high to maintain a low boil and cook another 15 minutes, or until a knife can be inserted into the potatoes with almost no resistance (this can sometimes take up to 25 minutes depending on the size of your potatoes).
Drain the water from the pot so that you are left with just the potatoes and garlic.
Add your potatoes and garlic to a large bowl. Mash the potatoes by using either a handheld potato masher, or a stand mixer set to a low-speed setting.
Once your potato mixture is mashed and all large chunks are gone, add your soy milk, coconut yogurt, salt, black pepper, onion powder, and nutritional yeast to the potatoes. Mix to combine everything, either with a stand mixer on low speed or with a wooden spoon.
Give it a quick taste test and add more seasonings or coconut yogurt if desired. You may also add more soy milk if you'd like your potatoes to be a thinner consistency. Add in your chives and mix again until just combined.
Serve and enjoy!