In a large bowl, toss grated potatoes with flour. Add mashed potatoes and stir until combined. In a separate bowl, whisk together milk and egg. Add milk mixture into the potatoes. Season with salt and pepper.
In a large skillet set over medium-high heat, heat olive oil. Using a spoon, drop in potato mixture, forming 6 patties about 2-inches in diameter. Fry on both sides until golden, about 3 to 4 minutes per side. Place on a paper towel-lined plate to soak up excess oil. Serve warm.
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