Combine the all-purpose flour, whole wheat flour, cornmeal, yeast, and salt in a stand mixer. Add the water, honey, and olive oil, then knead on medium-low speed until the dough is smooth, elastic, and clears the sides of the bowl.

Place the dough in a lightly oiled bowl and cover with plastic wrap. Let it rise in a warm, draft-free spot until doubled in size, about 1 hour.

Toss the sliced fennel, halved tomatoes, garlic, and oil on a rimmed baking sheet with salt and pepper. Roast at 425°F until the fennel is softened and the tomatoes begin to release their juices, about 15 minutes.

Press the air out of the dough and stretch it into a large rectangle on a piece of parchment paper. Use a rolling pin or your hands to ensure an even thickness so it bakes consistently.

Distribute the roasted vegetables across the surface, then top with the parmesan and oregano.

Slide the flatbread onto a preheated baking stone or inverted baking sheet. Bake until the edges are deeply golden brown and crisp, about 12 minutes.

Serve hot, while the crust is at its peak crispness.