Preheat the oven to 180°C. Cut the green parts of the leeks into large pieces and arrange on a roasting tray with three of the unpeeled smoked garlic cloves. Roast for about 15-20 minutes until the garlic is soft and the leeks are starting to char.
Melt a knob of butter in a saucepan and add half of the three cornered leeks. Once wilted add the roasted leeks and cover with boiling water. Leave to simmer for at least half an hour and season with salt and pepper. Strain the liquid, making sure you push all of the water out of the leeks with the back of a spoons. Discard the veg and keep the stock to one side.
Peel the roasted garlic cloves and add to a small saucepan with the milk. Heat until almost boiling and then remove from the hob and leave to infuse for at least half an hour.
Meanwhile chop the potatoes, keeping one aside for garnish, and the white parts of leeks into roughly a 1cm dice. Roughly chop some more of the three cornered leeks - making sure you keep a few whole for garnishes later. Melt a knob of butter in a heavy based pan and add the veggies. Place a piece of parchment paper over them and then put the pan lid on. Cook until the potatoes have softened, about 10 minutes.
Remove the parchment and add the stock to the pan. Cook for a few more minutes and then blend. Add milk until you have the consistency you want, add the smoked garlic cloves from the milk and blend again. Season and keep the soup warm whilst you make the garnishes.
Finely slice the potatoes and fry in oil until golden and crispy. Drain on kitchen paper and sprinkle with salt. Fry pieces of three cornered leek in the same way.
If you want to serve with some crusty bread, make a flavoured butter by crushing the remaining smoked garlic clove and mix with butter, a pinch of salt and some finely chopped three cornered leeks.
To serve dish up the soup and top with the crispy potatoes and leeks. Spead the garlic butter over some fresh bread and tuck in.