On a lightly floured board, roll pastry into a round 14 inches wide. Transfer pastry into a 12-inch tart pan with removable rim. Press into pan and trim off overhanging dough by pressing edge against pan's rim. Reserve pastry scraps for another use or discard. Prick the bottom all over with a fork, cover with plastic wrap, and freeze 30 minutes, or up to 1 week.
Meanwhile, trim and discard base of fennel, along with tough green stalks. Thinly slice fennel head crosswise.
Preheat oven to 350° (convection not recommended). Set a 10- to 12-inch frying pan over medium-low heat. Add olive oil, fennel, and shallots. Cook, stirring often, until vegetables are golden brown, about 30 minutes. Sprinkle with parsley, season with salt and pepper to taste, and remove from heat.
Remove tart crust from freezer and place (still in pan) in preheated oven. Bake until golden brown, about 20 minutes. Remove from oven and top evenly with parmesan, then fennel-shallot mixture, then tomatoes. Bake until cheese begins to turn pale golden brown, about 10 to 15 minutes longer. Remove pan rim, cut into wedges, and serve warm or at room temperature.
Do-ahead tips: Make dough through step Keep frozen, wrapped tightly, up to 1 week. Make fennel-shallot topping up to 3 days ahead. Refrigerate, covered, until ready to use.