1/3 cup pear nectar, apple juice or water
1 tablespoon lemon juice
8 slightly underripe pears, preferably Bosc or Bartlett, peeled and cut into 1/2-inch-thick slices
3/4 cup packed light brown sugar
2 tablespoons cornstarch
2 teaspoons freshly grated lemon zest
1 tablespoon finely minced fresh ginger
2 cups cranberries, fresh or frozen, thawed, coarsely chopped (see Tip)
1 teaspoon vanilla extract
1/3 cup reduced-fat sour cream
1 tablespoon lemon juice
1 1/3 cups all-purpose flour, plus more for dusting
2 tablespoons sugar, divided
1/2 teaspoon salt
1/4 teaspoon baking soda
1/4 cup canola oil
Position a rack in the center of the oven; preheat to 400?F. Coat a 3-quart nonreactive baking dish
To prepare filling: Combine pear nectar (or juice or water) and lemon juice in a large bowl. Toss pears with the juice. Whisk brown sugar, cornstarch, lemon zest and ginger in a nonreactive Dutch oven until combined. Drain the liquid from the pears into this mixture; stir until well blended. Heat the mixture over medium heat, stirring, just until it begins to boil, 2 to 3 minutes. Stir in the pears and cranberries and cook, stirring, until the mixture is steaming, about 2 minutes. Stir in vanilla. Spread the fruit in an even layer in the prepared baking dish.
To prepare crust: Combine sour cream and lemon juice in a small bowl. Place flour, 1 tablespoon sugar, salt and baking soda in a food processor fitted with a dough hook or chopping blade; process to combine. Drizzle in oil and process in quick pulses just until the mixture is the consistency of very fine crumbs, stopping and scraping the bottom and sides several times. Add the sour cream mixture; process in quick pulses just until incorporated and the mixture holds together when pressed between the fingers; do not overprocess. If the mixture seems dry, gradually add a little cold water, a teaspoon at a time, and pulse briefly several times just until the mixture is moistened and holds together.
Lightly dust a 14-inch-long piece of parchment or wax paper with flour. Turn the dough out onto the paper and let rest for 5 minutes. Knead briefly until the dough just comes together. Lightly flour the top and cover with a second sheet of paper. Roll or press the dough into the same shape as your baking dish, just slightly smaller. Discard the top sheet of paper. Invert the dough, centered, over the fruit. Discard the paper. Using a greased sharp paring knife, cut large decorative slashes in the dough to vent steam. Sprinkle the dough evenly with the remaining 1 tablespoon sugar. Place the baking dish on a rimmed baking sheet (to catch any overflowing juices).
Bake the cobbler until the top is golden brown, 40 to 50 minutes. Let cool on a wire rack for at least 20 minutes before serving. Serve warm or at room temperature.