Combine flour, cornmeal, baking soda, sugar, and salt together in a large bowl. Cut in butter with a fork or pastry blender until mixture looks crumbly. Stir in thyme, rosemary, and garlic powder. Sprinkle in water and vinegar; toss with a fork until a ball of dough forms.
Wrap dough tightly in plastic wrap. Freeze until firm, about 20 minutes.
Preheat oven to 375 degrees F (190 degrees C). Grease 2 baking sheets.
Cover a large cutting board with aluminum foil. Turn dough out onto aluminum foil, cover with plastic wrap, and roll out into a thin rectangle. Cut into smaller rectangles; transfer to baking sheets. Sprinkle with Parmesan cheese.
Bake in the preheated oven until golden brown and crispy, about 20 minutes.