Step 1Combine the flour, sugar and salt in a bowl. Cut in the cold butter with a pastry blender until the mixture resembles coarse meal. In a small bowl, lightly beat the egg yolk and stir in the ice water. Make a well in the center of the flour mixture and pour in the egg mixture. Gently mix with a fork until the dough just holds together. Shape the dough into a flat round and cover with plastic wrap. Refrigerate 1 hour before rolling out.
Step 2Alternately, using a food processor: Measure the flour, sugar and salt into the work bowl and process 2 to 3 seconds to mix. Scatter the butter over the top of the flour and pulse until the mixture is the texture of coarse crumbs. With the motor running, add the egg yolk and water through the tube and process just until the dough forms a ball.
Step 3Roll the chilled dough into a 10-inch circle on a lightly floured surface. Lift onto an 8-inch tart pan. Gently arrange the dough in the pan and pat onto the bottom and sides, trimming off excess dough around the edges.
Step 4Prick the bottom of the tart shell with a fork. Line the shell with aluminum foil, shiny side down. Fill with pie weights. Bake at 425 degrees for 12 minutes. Remove the pie weights and foil; bake an additional 7 to 10 minutes, until the shell is lightly browned. Remove from the oven and let cool to room temperature.
Step 1Combine 1 cup sugar and the water in a 10-inch nonstick skillet. Heat to simmering and cook until clear, 2 to 3 minutes.
Step 2Remove the syrup from heat and add the Merlot. Scrape the seeds from the vanilla bean and add to the wine mixture along with the pod. Bring to a low simmer and cook 15 minutes.
Step 3Add the figs to the simmering syrup, cut side down, and gently cook 5 minutes. Remove from heat. Let figs cool in the syrup for about 20 minutes.
Step 4Using a slotted spoon, transfer the figs from the syrup to a wire rack set over paper towels.
Step 5Cook the syrup over medium heat until it is reduced to 1 cup, about 30 minutes. Let it cool to room temperature.
Step 6While syrup is cooking, make the mascarpone filling. Combine the mascarpone, remaining 2 teaspoons sugar and lime zest. Chill the mixture until ready to assemble the tart.
Step 7To assemble, spread the mascarpone filling onto the bottom of the tart shell in an even layer. Arrange the figs on the filling in concentric circles. Sprinkle with mulberries. Brush the figs and mulberries with just enough syrup to glaze them. (Save remaining syrup to spoon over ice cream or pancakes.)