Melt butter and oil in a large saucepan. Add bacon and cook for a few minutes. Add onions. Cover and sweat on a gentle heat until the latter become soft but not coloured. Add stock and leave to simmer while you prepare the potatoes.
Add potatoes to saucepan and stir until the mix becomes sticky and thick. Season with pepper and a little salt.
Keep stirring and add milk slowly. Boil until the potatoes are soft. Garnish with parsley, taste and serve.