Wash and dry potatoes, then cut into evenly-sized pieces. Place into a large pot of cold, salted water and bring to a boil. Reduce heat and cook potatoes until fork tender. Remove from heat and drain. Transfer to a medium bowl and lightly mash until smooth and lump-free. Set aside.
To make candied garlic: Place water, sugar and garlic cloves into a medium pot and bring to a boil. Reduce heat and simmer for 15 minutes. Using a slotted spoon, transfer garlic cloves to a plate and set aside. Heat olive oil in a small pan over medium heat, then add minced garlic and whole garlic cloves that were set aside. Sauté for 3 minutes.
To make vinaigrette: In a small bowl, whisk together all ingredients. Set aside.
Add vinaigrette to mashed potatoes and gently stir. Garnish with the candied garlic and serve warm.
