Preheat oven to 350°. In a food processor, whirl flour, 2 tbsp. sugar, the cornstarch, and salt until combined. Add butter and 1/2 tsp. vanilla and pulse until fine crumbs form and dough just begins to come together. Press evenly into bottom and up sides of a 9-in. round tart pan with a removable rim.
Bake until edges are golden, 20 to 22 minutes. Let cool on a rack, then gently push tart crust from pan rim; set on a plate.
In a bowl with a mixer on high speed, beat crème fraîche, cream, remaining 2 tbsp. sugar, and remaining 1/2 tsp. vanilla until thick. Spread in cooled crust. Arrange strawberries in circles on top, alternating cut sides down and up.
Make ahead: Chill, loosely covered, up to 4 hours.
Note: Nutritional analysis is per serving.