Take the minced garlic and add a small amount of salt and mash the garlic in a small bowl. Add the egg yolk and with a hand mixer beat for 1/2 min. until the yolk has turned a pale yellow color.
Slowly add the oil while continuously beating. Continue beating until all the oil is incorporated and the mixture is the consistency of mayonnaise. Add in the mustard and lemon juice. Refrigerate until ready to use.
Have oil ready in a medium wok while the mussels are cooking.
Melt the butter in a large pot over medium heat then add the leeks, salt, and pepper, cook until the leeks are soft and transparent.
Add the mussels and white wine to the large pot, cover, and cook for 5-6 min. until they are opened. Remove the cooked mussels and keep warm discarding any mussels that have not opened. Reserve the liquid in the pot
Add the fries, in batches, to the hot oil and fry until golden brown, salt immediately when done, and keep warm.
Add 1/2 cup heavy cream to wine mixture, simmer to reduce for about 5-6 min.
Serve the mussels with the cream sauce and the pommes frites on top with a dollop of aioli. Garnish with a sprig of parsley.