Place warm water in a large bowl; sprinkle with yeast. Let yeast dissolve, about 2 minutes. Add flour, oil, and salt; combine.
Turn out dough onto a clean work surface, and knead until smooth and elastic, about 4 minutes. Coat a large bowl with cooking spray. Place dough in bowl; cover with plastic wrap. Set bowl in a warm place; let dough rise until doubled in size, about 30 minutes.
Place a pizza stone in oven; heat to 400 degrees. Dust a pizza peel or a baking sheet with 1 teaspoon cornmeal. On a lightly floured work surface, roll out one half of dough into a 12-inch circle. Transfer dough to peel, cover with plastic wrap, and let rest 15 minutes. Roll out second piece of dough; transfer to a baking sheet lined with parchment paper and dusted with remaining teaspoon cornmeal. Cover with plastic, and let dough rest 15 minutes.
Place currants and raisins in a small bowl. Cover with 1/4 cup warm water; set aside. Coat a wide 6-quart saucepan with cooking spray; set over medium-high heat. When hot, add onion; cook until translucent, about 2 minutes. Add escarole and vinegar; cook until escarole has wilted, 2 to 3 minutes. Drain currants and raisins; add to escarole mixture. Remove pan from heat; set aside.
Remove plastic from the dough on peel. Sprinkle half of Gruyere over the dough, leaving a 1-inch border. Sprinkle nutmeg over cheese, and cover with half of escarole mixture. Top with 1 tablespoon grated Parmesan and 1 tablespoon sliced almonds. Transfer pizza to stone in oven; cook until crust is golden and crisp, 15 to 20 minutes. Transfer to a wire rack to cool slightly.
Slide remaining dough onto peel; repeat step 5. Cut each pizza into 4 wedges; serve.