Preheat the oven to 400 degrees F.
Roast the garlic: Peel and discard the outer papery layers of the whole garlic head. Leave the skins intact of the individual cloves. Using a sharp knife, cut ¼ inch off from the top of the cloves so that the individual cloves of garlic are exposed. Place garlic in a medium piece of foil and drizzle the top of the garlic with olive oil then loosely wrap in the foil and place on a small sheet pan. Roast in the oven for 40 minutes until very fragrant. Allow garlic to cool for 5 to 10 minutes before removing foil. (This can be done up to 2 days ahead of time and roasted garlic can be kept in the fridge.)
Set out the milk: Bring the milk to room temperature white you cook the potatoes. I typically add mine to a bowl and let it sit near the oven where it is nice and warm.
Brown the butter: Add the butter and chopped sage to a medium saucepan over medium heat. Once melted, whisk constantly; the butter will begin to crackle, then foam. After a few minutes, the butter will begin to turn a golden amber color. As soon as the butter turns brown and gives off a nutty aroma, 5 to 8 minutes total, remove from the heat and keep the butter in the pan. (The sage should be nice and crispy too!)
Cook the potatoes: While the garlic is roasting in the oven, add the potatoes to a large pot and cover with cold water by at least 1 inch then add 2 teaspoons kosher salt. Cover and bring to a boil over high heat. Once boiling, remove the lid and boil until potatoes fork-tender, 20 to 30 minutes. Drain and return to the pot.
Whip the potatoes: Use your fingers to squeeze the roasted garlic from the skin and add it directly to the pot with the potatoes, then add in 4 tablespoons of the brown butter (reserving about 2 for pouring on top of the potatoes later), the Greek yogurt, 1 cup milk, 1 teaspoon kosher salt and as much freshly ground black pepper as you’d like.
Use a handheld electric mixer to whip the potatoes on medium speed (or use a potato masher) until smooth and creamy, about 2 minutes. If you’d like creamier potatoes, add additional milk (¼-½ cup at a time) and whip again for 20 to 30 seconds. Taste and adjust the salt and pepper, if necessary.
Serve: Transfer mashed potatoes to a serving bowl or dish and drizzle with remaining 2 tablespoons brown butter, crispy sage and a sprinkle of flaky Maldon salt, if desired. Serve immediately.