Step 1

Whisk crème fraîche and orange peel in small bowl. Cover; chill. Roll out pastry on lightly floured surface; trim corners to create circle. Place on plate. DO AHEAD: Crème fraîche and crust can be prepared 1 day ahead. Cover separately and chill.

Step 2

Preheat oven to 400°F. Mix plums, 2 tablespoons sugar, lemon juice, lemon peel, nutmeg, and seeds from vanilla bean in large bowl. Let stand 30 minutes.

Step 3

Melt butter in heavy ovenproof 9-inch-diameter skillet over medium heat. Sprinkle remaining 2/3 cup sugar evenly over melted butter. Tightly arrange plums, cut side up, in concentric circles in skillet (plums will appear slightly uneven but will soften while cooking, creating even layer). Drizzle accumulated juices from bowl over top. Cook over medium heat, shaking skillet gently to prevent sticking. Continue cooking until syrup turns deep red, pressing plums slightly to form compact layer, about 35 minutes. Remove skillet from heat; cool 10 minutes.

Step 4

Slide crust atop plums in skillet. Press crust edges down around plums at edge of skillet. Cut several slits to allow steam to escape. Bake until golden brown, about 30 minutes. Cool tart completely in skillet.

Step 5

Rewarm in skillet set over high heat to loosen, about 3 minutes. Place large platter over skillet. Using oven mitts, hold skillet and platter together and invert, allowing tart to settle onto platter. Slowly lift off skillet. Let stand at least 30 minutes and up to 4 hours at room temperature. Serve with orange crème fraîche.