Blanch the green beans and carrots separately in a large pot of boiling salted water for 4 to 5 minutes. Drain, and shock in ice water to cool. Put all of the ingredients in a large glass bowl. Toss to coat the vegetables evenly with the olive oil. Refrigerate for 8 hours. Serve in shallow glass dishes with the crackers.
In a mixing bowl, combine the flour, cayenne, salt, mustard, and butter. Mix until mixture resembles a coarse crumb-like mixture. Add the cheese and mix well. Add the water a tablespoon at a time and let sit for 1 minute. Either using a fork or your hands, carefully press the mixture together to form a soft ball. Wrap in plastic wrap and refrigerate for at least 30 minutes. Remove the dough from the refrigerator and place it on a lightly floured surface. Roll the dough out on the floured surface into a rectangle 16 by 12 inches in diameter and 1/8-inch thick. Cut the dough into 3 by 1-inch strips. Place on a parchment lined baking sheet and bake in a preheated 350 degree oven until golden brown and crispy, about 10 to 12 minutes. Remove from the oven and cool completely.