Place the potatoes, garlic, and the 1 teaspoon kosher salt in an 8-quart pan and fill with enough water to cover the potatoes. Bring the water to a gentle boil and cook until the potatoes are just tender. Drain the potatoes, return them to the pot, and stir over medium heat for 1 minute to dry the potatoes.

Add 3 tablespoons of the cornmeal and the parsley and mash everything together with a potato masher, leaving the mixture chunky.

Whisk together the egg, egg yolk, milk, and 1 tablespoon of the oil in a small bowl. Stir the mixture into the potatoes and season with salt and pepper. Spread the potatoes out on a large plate, cover with plastic wrap, and refrigerate for at least 1 hour or up to 4 hours.

Preheat the oven to 350 degrees F.

Form the chilled potato mixture into 16 cakes about 3/4 inch thick. Put the remaining 5 tablespoons cornmeal in a shallow dish and coat the potato cakes in the cornmeal.

Heat the remaining 2 tablespoons olive oil in a 10-inch skillet over medium heat. Add the potato cakes, in batches, and brown them on both sides.

Transfer the potato cakes to a baking sheet and bake until heated through, 10 to 15 minutes.