Preheat oven to 350 degrees. In a food processor, whirl flour, 2 Tbsp sugar, 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 9-inch round tart pan with a removable rim.
Bake until edges are golden, 20-22 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 creme fraiche, 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. Chill, loosely covered, up to 4 hours.
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