Preheat oven to 400° with a rack set in lower third of oven and no rack above.
Line a baking sheet with parchment paper. On a lightly floured work surface, unfold dough; if using 2 sheets, stack them. Roll (if needed for size) into a 10- by 12-in. rectangle, smoothing creases; trim dough to neaten edges. With both hands, gently lift dough to lined baking sheet. With a small knife, lightly score a 1/2-in. border around dough. Brush off excess flour. Freeze 15 minutes to firm.
Brush border of dough with beaten egg. Bake until puffed and lightly browned, 10 to 15 minutes. Press down on center of pastry with a metal spatula to flatten it.
Meanwhile, bring a large saucepan of water to a boil. Chop 1 tbsp. carrot tops. Tear more tops into small pieces to make 1 tbsp.; set tops aside. Peel carrots, then set on a work surface and pull a vegetable peeler along them to create 4 cups ribbons; save end pieces for other uses.
Boil carrot ribbons until barely tender, 1 minute. Drain, transfer to a bowl of ice water, and let cool. Drain ribbons and pat very dry; toss in a bowl with chorizo, oil, salt, and pepper.
In a food processor, whirl cream cheese with 2 tbsp. feta until smooth, scraping inside of bowl.
Drop small spoonfuls of cream cheese mixture over center of pastry and smear gently with fingers (it won't spread to cover pastry). Sprinkle with reserved chopped carrot tops. Arrange carrots evenly over cream cheese and scatter with remaining feta. Bake until pastry is well browned, 15 to 20 minutes.
Let tart cool briefly on a rack, then scatter reserved torn carrot tops on top.
Wine pairing: A tangy pink sparkler like Gloria Ferrer 2011 Brut Rosé (Carneros; $47). Its red fruit and spice love the chorizo, and its yeastiness links to the pastry. --Sara Schneider