Preheat the oven to 425 degrees F. Spray two 24-cup mini muffin tins with cooking spray.
Place the russets into a large pot and cover with cold water. Bring to a simmer over medium heat and cook until halfway done, 5 to 7 minutes. Drain, then use a kitchen towel to carefully remove skins. Let cool for 15 minutes.
Grate the par-cooked russets into a large bowl. Grate the red potatoes and add them to the bowl as well. Add the salt, pepper, flour and olive oil. Gently combine by hand.
Scoop one tablespoon of the potato mixture into each muffin cup, pressing flat with your fingers. Bake until brown at the edges, 15 minutes, then flip so that each side gets golden brown! Spray the tops with more nonstick spray and sprinkle with salt. Return to the oven and bake until browned, another 12 to 15 minutes.
Serve with ketchup and mustard for dipping.