Crust: Sift the flour, sugar, and salt into a large bowl. Add the butter and shortening. Rub the fats between your fingertips and thumbs, or use a pastry blender, until the mixture resembles coarse crumbs. One tablespoon at a time, work in enough ice water just until the dough comes together, being careful not to overmix.
Shape into a smooth ball of dough, flatten into a disk, and wrap in plastic wrap. Refrigerate for at least 30 minutes and up to 2 days.
Cobbler: Preheat oven to 350 degrees F.
To prepare the cobbler, place the rhubarb and apples in a large, heavy saucepan. Add olive oil, 1 tablespoon sugar and water. Stir over high heat until the sugar has started to dissolve, 1 to 2 minutes. Reduce the heat to medium and cook, stirring often, until the fruit has exuded some of its liquid, about 5 minutes. Transfer mixture to a large bowl with the remaining 4 tablespoons sugar, flour, lemon zest, and salt. Cool slightly; pour into a lightly buttered 1-quart baking dish, and dot with the slivers of butter.
When ready to use crust, sprinkle a little flour on a smooth work surface, and using a rolling pin or dowel, roll the pie dough about 1/8-inch thick and large enough to cover the baking dish.
Cover cobbler with pie dough. Bake for 35 to 40 minutes, until top is golden. Let cobbler cool for 15 minutes before serving. Serve with vanilla ice cream.