How to Make It
In a large saucepan, cover the potatoes with water and bring to a boil. Add a large pinch of salt and boil over moderately high heat until the potatoes are tender, about 25 minutes. Drain well.
Add the stock, cream and milk to the saucepan and bring to a boil over moderate heat. Stir in the butter, garlic and nutmeg. Add the potato pieces a few at a time and with an immersion blender, puree until very smooth. Alternatively, blend the soup in a food processor. Season with pepper and keep warm.
In a medium skillet, cook the bacon over moderate heat until crisp, about 3 minutes per side. Transfer the bacon to paper towels to drain, then break into pieces. Pour off most of the fat from the skillet. Add the sausages to the skillet and cook over moderate heat, turning, until browned and cooked through, about 4 minutes. Chop the sausages.
Fill a medium, deep skillet with water and bring to a boil; reduce the heat to maintain a gentle simmer. Crack each egg into a small bowl and tilt the egg into the simmering water. Poach over moderately low heat, pushing the eggs a few times with a slotted spoon so they don't stick to the skillet, until the whites are just firm and the yolks are runny, about 3 minutes.
Ladle the soup into shallow bowls. Top with the bacon, sausage and well-drained poached eggs. Garnish with the chives and pass the ketchup at the table.