In a medium-sized stove pot, melt the butter, do not let it burn or change color.
Add the chopped onions and garlic. Saute' for 5 minutes minutes until shiny and velvety looking.
Add the chopped leeks, including the leaves, and cook for another 4 minutes.
Add the chopped potatoes and cook for about 30 minutes, until the potatoes are 'almost', but not 'completely' cooked through.
Now place a medium-sized tall pot on the stove and add the milk. Bring to a very low boil, keeping an eye on it and stirring so as not to burn.
Add haddock to the hot milk to poach for no more than 4 minutes. At the same time add the thyme, bay leaves, and bouquet garnis to marry with the milk and fish flavors.
When poaching is finished, remove the haddock from the hot milk; place it in either a large bowl or a large plate, and allow it to cool.
Once cooled, using your fingers, 'flake' the fish by pulling apart chunks of fish.
When the potatoes are nearly done cooking, add the hot milk that you used to poach the fish.
Add the chunks of smoked haddock.
Add cream, chives, and Italian parsley. (optional: add a few drops of liquid smoke). Bring to a soft boil and then serve immediately while piping hot!
Buon Appetito!