In a small bowl, mix together soy milk and cider vinegar. The mixture will clabber and become like buttermilk. Don’t panic, this is what it’s supposed to do. Set aside and let it be. In a large mixing bowl, sift unbleached flour, whole wheat flour and sea salt into a large mixing bowl. Add the Miyoko's and work in quickly, so everything comes together and becomes coarse, like damp sand. Pour in clabbered soy milk and mix together with a light hand, until it just coalesces into a dough. Wrap well in plastic wrap or foil and chill for 2 hours or up to several days.
Pour the halved grape tomatoes into a medium-sized nonreactive bowl, such as glass or ceramic. Add fresh chopped rosemary, sea salt and pepper and drizzle in 1 tablespoon of the olive oil. Toss lightly and set aside.
Heat remaining tablespoon of olive oil in a large skillet set over medium-high heat. Add sliced onions and minced garlic. Stir and saute for a few minutes or until the onions start to darken. Reduce heat to medium and continue cooking the onions, stirring often, for another 10 to 15 minutes, until they darken, caramelize and smell sweet. Add the chopped kale or chad by the handful. Give everything a stir. The greens should start to wilt after a minute or two. Reduce heat to low and continue stirring gently for another few minutes, until the greens are tender and reduced in volume but still keep their bright color. Allow to cool slightly.
To assemble: Heat oven to 400 degrees. Line a baking sheet with parchment paper and sprinkle generously with flour. Roll out pastry onto the floured parchment, forming a 12-inch round, about 1/4 inch thick. Round is relative, round-ish will do. Sprinkle chopped olives onto the center of the pastry, creating a circle about 6 inches across, leaving a 3-inch border of exposed pastry all the way around. Cover the olives with the greens, smoothing gently. Top the greens with the halved tomatoes. Drizzle any juices left in the bowl onto the tomatoes.
Gently lift one edge of the exposed dough and fold towards the center, to the outer edge of the greens, creating a loose pleat of pastry. Continue working all the way around, so all the pastry is folded inward. Leave about 3 to 5 inches of tomatoes peeking through the center. Bake for 30 minutes, or until crostata is golden brown. Let the crostata rest for 20 to 30 minutes before serving. Slice into wedges and enjoy.