Roll out pie dough on a well-floured surface or between two pieces of parchment paper. Lay dough over tart shell, allowing excess dough to hang over tart pan walls. Gently press dough into tart pan. Using a rolling pin, roll over pie dough on tart border to cut the crust. Peel away excess dough. Place tart pan in freezer and freeze until firm, about 30 minutes. Meanwhile, preheat oven to 375.
Place frozen tart shell (in tart pan) on a baking sheet. Spray a large enough piece of tinfoil to cover tart with cooking spray. Gently press tinfoil, spray side down, over tart. Fill with pie weights and bake until top edge starts to color, about 30 minutes.
Remove tart shell from oven and remove foil and weights. Sprinkle parmesan over pie crust. Return to oven and bake about 10 minutes. Remove from oven and allow to cool.
While shell bakes, in medium bowl, toss tomatoes with olive oil, garlic, salt, pepper, and sugar. Spread tomatoes cut side up on a baking sheet. After removing tart shell from oven, roast tomatoes until slightly shriveled, about 45 minutes.
Place tomatoes on tart, overlapping. Sprinkle feta evenly over tart. Return to oven and bake until crust is golden and cheese just starting to brown, about 20 minutes.