Tomato Tarte Tatin

Preheat oven to 425°F. Bring large saucepan of water to boil. Cut shallow X in bottom of each tomato. Add 4 tomatoes to boiling water. Blanch tomatoes just until skins at X begin to peel back, 15 to 30 seconds. Using slotted spoon, transfer blanched tomatoes to bowl of ice water to cool quickly. Repeat with remaining tomatoes. Peel tomatoes. Cut out cores, halve lengthwise, and remove seeds.
Spread butter over bottom of 9 1/2-inch diameter, 2- to 3-inch-deep ovenproof skillet (preferably cast-iron). Sprinkle 3/4 cup sugar over butter. Arrange tomato halves, rounded side down and close together, in concentric circles in skillet to fill completely.
Place skillet over medium heat. Cook until sugar and butter are reduced to thickly bubbling, deep amber syrup (about 1/4 inch deep in bottom of skillet), moving tomatoes occasionally to prevent burning, about 25 minutes. Remove skillet from heat. Immediately drizzle vanilla over tomatoes. Top with pastry round. Using knife, tuck in edges of pastry. Cut 2 or 3 small slits in pastry. Place skillet in oven and bake tart until pastry is deep golden brown, about 24 minutes.
Cool tart in skillet 10 minutes. Cut around sides of skillet to loosen pastry. Place large platter over skillet. Using oven mitts as said, hold skillet and platter firmly together and invert, allowing tart to settle onto platter. Carefully lift off skillet. Rearrange any tomato halves that may have become dislodged.
Serve tart warm or at room temperature with whipped cream.