Preheat oven to 450°F (230°C). Heat olive oil in a non-stick skillet over medium-high heat; add sliced potatoes and sauté for 10 min., until slightly softened. Season with 1/2 tsp salt, pepper and smoked paprika; toss in chopped parsley. Set aside.
Whisk together the eggs and milk and season with 1/2 tsp salt and pepper. Spread potatoes evenly in the tart shell and sprinkle shredded Cheddar cheese overtop. Pour eggs over the potatoes and jiggle to settle.
Bake for 15 minutes; turn oven down to 350°F (180°C) and bake for another 15 min. Serve immediately or let cool to room temperature, wrap and refrigerate until needed. To reheat, slice and warm for 10 min. before serving.
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