In a food processor combine flour, yeast, sugar, and 3/4 tsp. salt. Add the warm water and 3 Tbsp. olive oil; pulse until combined and a dough forms. Transfer dough to a lightly floured surface. Knead until smooth, 2 to 3 minutes.

Transfer to a greased medium bowl; turn to grease surface of dough. Cover and let rise until nearly double, 1 to 11/4 hours. Place a pizza stone in a cold oven. Preheat oven to 450°F.

In a large skillet heat butter over medium-high until it starts to brown and smells nutty, 4 minutes. Add mushrooms and garlic. Cook and stir until tender and browned and liquid has evaporated, 6 to 8 minutes.

On a lightly floured surface, roll dough into a 12×10-inch rectangle. Transfer to a flat baking sheet sprinkled with the cornmeal. Reshape dough as needed. Top with mushroom mixture, grapes, goat cheese, and walnuts. Slide pizza onto stone in oven.

Bake until crust is golden brown, 18 minutes. Top flatbread with herbs and drizzle with honey. Serves 8.