Make a cut around the corn husk at 2 inches from the end. Tear off the husk along the cut. (See photos. This step is to make a handle on each corn.) Remove the hair inside.
Wrap up each prepared corn with foil and put directly on the oven rack. Bake for 30-35 minutes.
While the corn is baking, make the aioli. Smash up the garlic with sea salt in a pestle and mortar (or use the end of a rolling pin in a metal bowl).
Place egg yolk and mustard in a medium bowl. Whisk until blend. Start adding oil bit by bit, stir vigorously till creamy. Make sure to blend well each time you add a bit oil into the egg yolk mixture.
When all the oil has gone in and the mixture is thickened, add lemon juice and the smashed garlic with salt. Mix well. Add 2 tablespoons chopped parsley. Stir until even. Taste, season with more salt, pepper or lemon juice if needed.
When corn is done, let cool for a few minutes.
Coat 2 tablespoons aioli on each corn. Make sure that all sides are covered. Sprinkle with paprika and Parmesan cheese. To finish off, top with the remaining parsley.