Add the potatoes to a large pot and cover with water. Add 2 tsp salt and bring to a boil and cook until the potatoes are very fork-tender, about 15 minutes.
Once the potatoes are tender, drain the potatoes and let sit in the colander to release the steam (this will help to have any excess moisture removed).
After moisture has been released, add to a large mixing bowl (if using a hand-held mixer) or a stand mixer with the whisk attachment.
Once the garlic is cool enough to handle, squeeze out the cloves into the mixing bowl with the potatoes.
Next, add the butter, coconut milk, broth and whisk on medium-low speed until smooth and most of the liquid has been absorbed. Add the remaining 2 teaspoons of salt and the pepper and whisk again on medium-low speed until the potatoes are well-whipped and creamy.
Add the chives and gently fold into the potatoes.