If you don't like rolling out a crust, this one's for you. You just press it into the pan.
Crust:
· 7 tablespoons unsalted butter, melted* (save light-colored pan to melt butter for filling)
· 1/3 cup sugar
· 1/4 teaspoon vanilla extract
· 1 cup plus 1 tablespoon all purpose flour
· Pinch of salt
Filling:
· 1/2 cup sugar
· 2 large eggs
· Pinch of salt
· 1/4 cup all purpose flour
· 1 teaspoon vanilla extract
· 1/2 cup (1 stick) unsalted butter*
· 2 6-ounce containers fresh raspberries or 2 peaches, sliced
For crust:
Position rack in center of oven and preheat to 375°F. Using rubber spatula or fork, mix melted butter, sugar, and vanilla in medium bowl. Add flour and salt and stir until incorporated. Transfer dough to 9-inch-diameter tart pan with removable bottom. Using fingertips, press dough evenly on bottom and up about 3/4" the sides of pan.
Bake crust until golden, about 15-18 minutes (crust may puff slightly while baking). Transfer crust to rack and cool in pan. Maintain oven temperature.
For filling:
Whisk sugar, eggs, and salt in medium bowl to blend. Add flour and vanilla; whisk until smooth. Cook butter in heavy small saucepan over medium heat until deep nutty brown (do not burn), stirring often, about 6 minutes. Immediately pour browned butter into glass measuring cup (to keep from burning). Gradually whisk browned butter into sugar-egg mixture; whisk until well blended.
Arrange raspberries/peaches into bottom of cooled crust. Carefully pour browned butter mixture evenly over berries. Place tart on rimmed baking sheet. Bake tart until filling is puffed and golden and tester inserted into center comes out clean, about 30-35 minutes. Cool tart completely in pan on rack.
Remove tart pan sides. Place tart on platter. Cut into wedges and serve.
DO AHEAD: Can be made 1 day ahead. Cover and store at room temperature, but it might get soggy overnight.
*Test-kitchen tip: When browning butter, use a saucepan with a light-colored bottom so that you can gauge the color of the butter.