In a large sauté pan, warm the olive oil over medium-high heat. Add the Brussels sprouts, shallots and carrots, and stir. Cook, stirring often, for about 5 minutes, until the vegetables are wilted and browned. Add the thyme, maple syrup, 1/2 teaspoon salt and pepper, and stir for another minute. Scrape the vegetables into a medium bowl and let cool. When cooled, stir in the walnuts and shredded cheese.
Line a large sheet ban with parchment paper. Preheat oven to 400 degrees.
In a large bowl, combine the whole wheat pastry flour, unbleached flour and 1 teaspoon salt. Stir to mix well.
Use the coarse holes of a grater or a pastry cutter to shred or cut the butter into the flour mixture. Toss the mixture and mix with your hands for a few seconds, leaving the butter in small pieces.
In a cup, combine the ice water and vinegar. Using a fork to toss the flour mixture, drizzle in the water mixture until the flour is all moistened. Stir and gently turn and knead with your hands, just until a dough is formed. If the dough is dry, drizzle in a tablespoon of cold water just to make a firm but flexible dough.
Divide the dough into 6 equal pieces, and form each piece into a disk shape. On a floured work surface, roll each round out into a 7-inch circle.