Place potatoes in a medium sauce pan and cover with water by 1-inch.
Stir in 1/2 teaspoon salt. Bring to a boil over high heat. Reduce heat to medium and simmer for 15 – 18 minutes until potatoes are fork tender.
Drain, reserving 1/4 cup cooking liquid. Place potatoes in a bowl with reserved liquid. Mash potatoes using a potato masher or ricer.
Measure out 2 cups mashed potatoes and place in medium bowl. Add cheese, beaten egg, shallot, parsley, olive oil, remaining salt, and pepper. Stir to blend.
Preheat the oven to 375°F. When hot, scoop out potato mixture using a 1/4-cup measure. Arrange 4 scoops on each side of the griddle. Cook for 5 to 6 minutes per side, until golden and crispy on the outside, and hot on the interior. Serve hot.