*3 large egg yolks*
*1 cup sugar*
*3/4 cup fresh lime juice*
*6 tablespoons butter, cut into 6 pieces*
*1/2 cup unsalted butter, room temperature*
*1/4 cup sugar*
*1 large egg yolk*
*1 1/4 cups all-purpose flour*
*1 large pinch salt*
*1 6-ounce container of fresh raspberries*
*1 6-ounce container of fresh blackberries*
*1 6-ounce container of fresh blueberries*
Set fine metal strainer over medium bowl and set aside. Whisk eggs, egg yolks, and sugar in another medium metal bowl to blend. Whisk in lime juice. Set bowl over large saucepan of gently simmering water (do not allow bottom of bowl to touch water). Whisk constantly until curd thickens and instant-read thermometer inserted into curd registers 178°F to 180°F, about 6 minutes. Immediately pour curd through prepared strainer set over bowl. Add butter to warm strained curd; let stand 1 minute, then whisk until blended and smooth. Press plastic wrap directly onto surface of curd, covering completely. (This helps a film to not form on the curd.) Refrigerate until cold, about 4 hours. DO AHEAD Lime curd can be made up to 2 days ahead. Keep chilled.
Using electric mixer, beat butter and sugar in medium bowl until well blended, 1 to 2 minutes. Add egg yolk; beat to blend. Add flour and salt and mix on low speed until mixture resembles large peas. Using hands, knead in bowl just until dough comes together.
Transfer dough to 9-inch-diameter tart pan with removable bottom. Break dough into pieces, then press dough evenly up sides and onto bottom of pan. Cover and chill 1 hour. DO AHEAD Can be made 1 day ahead. Keep chilled.
Preheat oven to 350°F. Uncover crust and bake until golden brown, about 35 minutes. Cool completely in pan on rack.
Remove sides from tart pan and place crust on plate. Spread lime curd evenly in baked crust. Arrange raspberries in one circle then blackberries in 2 concentric circle just inside edge of tart. Mound blueberries in center of tart.
Do ahead: Tart can be made up to 8 hours ahead; chill uncovered.