Make a cut around the bright green husks of the corn at 2 inches from the end. Tear off the husks along the cut. (See photos. This step is to turn the corn cob into a handle.) Remove the silk inside.
Wrap up each prepared ear of corn with aluminum 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 with 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 blended. Start adding oil, bit by bit, stirring 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 evenly mixed. Taste, season with more salt, pepper, or lemon juice if needed.
When corn is done, let cool for a few minutes.
Coat each ear of corn with 2 tablespoons aioli. Make sure that all sides are covered. Sprinkle with paprika and Parmesan cheese. To finish off, top with the remaining parsley.