Place all the sauce ingredients in a Mason jar. Mix for several seconds using a handheld mixer, resting the beater on the bottom and then slowly drawing it up to thicken the mixture. The sauce is ready when it is nice and thick. Season with salt and pepper. (Do not cook the sauce. The poached eggs will heat it up enough.)
In a saucepan, add the vinegar to a good quantity of water and bring to a boil. Carefully break the eggs into coffee cups and then place them in the water by gently sliding them out of the cups. Cook for 4 to 5 minutes. Place the cooked eggs on a sheet of paper towel. Set aside.
While the eggs are cooking, melt a little lactose free butter in a skillet. Cook the leeks for a few minutes. Season with salt and pepper. Set aside.
Toast the English muffins. Add one or two slices of ham to each half. Add an egg and drizzle with the sauce. Top the sauce with some leeks. Season with pepper and enjoy!