Blend flour, sugar, and salt in processor until combined. Add butter; using on/off turns, cut in until mixture resembles coarse meal. Add egg yolk and wine; using on/off turns, mix just until moist clumps form. Gather dough into ball; flatten into disk. Wrap in plastic and chill at least 40 minutes and up to 2 days.
Position rack in center of oven and preheat to 375°F Roll out dough between 2 sheets of parchment paper to 12-inch round. Remove top sheet of parchment and transfer dough, with bottom parchment, to rimmed baking sheet. Place pear slices, 1 tablespoon sugar, and flour in large bowl; toss to combine. Spoon pear mixture into center of dough, leaving 1-1/2-inch border. Using parchment as aid, fold up outer edge of dough over edge of filling. Bake until pears are tender, about 20 minutes.
Meanwhile, boil 1 cup wine, 1/2 cup water, and remaining 1/2 cup sugar in medium saucepan until syrup is reduced to 1/2 cup, about 10 minutes.
Reduce oven temperature to 325°F Drizzle half of syrup over filling. Continue baking tart until juices are bubbling thickly, about 20 minutes. Cool.
Whisk 2 tablespoons wine into remaining syrup. Cut tart into wedges. Drizzle with syrup.
Serve with ice cream.