Preheat oven to 400ºF. Place the potatoes and 1 Tbsp. of salt in a medium pot, add water to cover and bring to a boil. Reduce to a simmer and cook for 10 minutes or until tender. Drain potatoes and cool slightly.
In a small bowl, mix together the red onion and red wine vinegar. Set aside.
Slice off the very end of each potato, then cut each potato into 2-3 equal slices. Overall yield should equal approximately 48 potato slices.
Heat the canola oil over medium-high heat in a large frying pan. Sauté half of the slices in hot oil until brown on both sides, about 2-3 minutes per side. Remove to paper towels to drain, sprinkle with salt and pepper, and repeat with remaining potatoes.
Place potatoes on a large baking sheet and top with 1 tsp. shaved Mahón. Place in top rack of oven until cheese just begins to soften, about 1-2 minutes.
Meanwhile, drain the minced red onion in a fine sieve, then rinse with cold water. Press out any excess water and return onion to bowl. Remove potatoes from oven and top each slice with 1/2 tsp. of red onion relish, garnish with parsley if desired, and serve.