In a large skillet, melt 2 tablespoons butter over medium-low heat. Add the onions and sugar; cook, stirring occasionally, until onions turn dark golden brown - about 30 minutes.
Place potatoes in a 4-quart saucepan. Cover with salted water. Cook potatoes over medium-high heat until very soft - about 25 minutes. Drain potatoes and return to saucepan.
Using a potato masher or an electric hand mixer on low speed, mix together potatoes, remaining 4 tablespoons butter, the milk, the salt, and the pepper until well combined. Fold in caramelized onions and serve.