Place the potatoes in a large pot of cold, salted water. Bring to a boil and cook until fork tender.
In the meantime, melt 2 tablespoons of butter and the olive oil in a large sauté pan over medium heat. Add onions, 1/4 teaspoon salt and the sugar and stir frequently, until onions are golden brown and caramelized, about 30-40 minutes. If the onions get too dry, add a small amount of water to deglaze the pan. Set aside.
While the potatoes and onions are cooking, heat the half and half, garlic, bay leaf, and remaining 2 tablespoons of butter in a small saucepan over medium heat.
When done, drain the potatoes and return them to the hot, dry pot. Stir them over low heat for 2 minutes until they are dry. Pass the potatoes through a ricer into a large bowl.
Discard the garlic and bay leaf from cream. Gently stir in the hot cream a little at a time until the potatoes are smooth and creamy. You may not need to use all of the liquid.
Set aside a small amount of the caramelized onions for garnish and stir the remaining onions into the mashed potatoes. Crumble the goat cheese into the potatoes and stir to combine well. Season with salt and black pepper to taste.
Spoon the mashed potatoes into a serving bowl and garnish with the remaining caramelized onions. Serve hot.