Put the potatoes in a large saucepan and fill with water to cover by 1 inch. Salt the water until it tastes salty. Bring to a boil over medium heat and cook until potatoes are tender when pierced with the tip of a knife, 25 to 30 minutes. Drain in a colander, shaking off the excess water. Return the potatoes to the pot.
Combine the clarified butter and garlic in a small saucepan over medium-low heat. Gently roast until the garlic is soft and lightly golden, taking care not to let the cloves brown too much, 10 to 15 minutes. Add the milk, bring to a simmer over medium heat and then remove the pan from the heat. With a slotted spoon, transfer the garlic cloves to the drained potatoes.
Break down the potatoes and roasted garlic slightly using a potato masher. Pour in the hot milk-butter mixture and mash until combined and smooth. Season to taste.
Heat 1 inch of oil to 350 degrees F in a high-sided pan.
In a small bowl, soak the sliced shallots in the buttermilk. Place the rice flour in a medium bowl and season with salt and pepper. Using tongs, transfer the shallots from the buttermilk to the rice flour and toss to coat. Fry the shallots in batches until just golden brown, 2 to 3 minutes. With a slotted spoon or spider, remove to a paper-towel-lined plate to drain.
To serve, mound the mashed potatoes in a serving bowl and sprinkle with the fried shallots.