In a medium saucepan, melt the butter over medium high heat. Add the shallots and bring to a simmer; reduce heat to low and cook, stirring occasionally, 20-25 minutes or until shallots turn golden brown and begin to crisp. (They will darken as they cool) Using a slotted spoon, transfer the shallots to a plate lined with a paper towel. Sprinkle with salt and let cool. Once cool, shallots can be kept in an airtight container for several days.

Place garlic and potatoes in large pot and add just enough water to cover. Bring to a boil over high heat and cook 15 to 20 minutes, or until potatoes are tender.

In a large mixing bowl, stir together the yogurt, horseradish, and 1/4 teaspoon salt. Add the potatoes and garlic cloves. Beat with an electric mixer until smooth. Season with additional salt to taste.

Immediately before serving, top potatoes with crispy shallots and fresh parsley.