Preheat oven to 425°F. Blend cream and 2 ounces feta in a food processor until smooth; season with salt and pepper.
If using 14-ounce package of puff pastry, cut in half and roll out each half on a lightly floured surface into a 16x10" rectangle. (If using 17.3-ounce package, use 1 sheet of pastry for each tart.) Transfer each piece of pastry to a parchment-lined baking sheet. Using a paring knife, lightly score pastry (do not cut all the way through), leaving a 1" border.
Spread feta mixture over pastry, dividing evenly and staying within border. Arrange artichoke hearts over feta mixture and crumble remaining 2 ounces feta over; drizzle with oil. Brush pastry border with egg.
Bake tart until pastry is puffed and beginning to brown, 10-15 minutes. Reduce oven temperature to 375°F and continue to bake until pastry is deep golden brown and cooked through, 20-25 minutes longer. Serve warm or at room temperature.