Prep: 30 minutes; Rest: 1 hour, 15 minutes; Bake: 14 minutes.
Combine 1 cup warm water, yeast, and sugar in a glass measuring cup, and stir to mix; let stand 10 minutes or until frothy.
In a separate large bowl, whisk together flour, cornmeal, and sea salt. Make a well in the center, and add olive oil and yeast mixture; mix thoroughly until it forms a stiff dough. Turn dough out onto a lightly floured surface, and knead until smooth and elastic (about 10 minutes). Place in a lightly oiled bowl, turning to grease top. Cover with a damp cloth, and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk.
Preheat oven to 450°. Punch dough down, and divide into fourths; let rest 15 minutes. Roll each portion into a flat 10- to 12-inch round on a surface dusted with cornmeal. Transfer each round onto a baking sheet dusted with cornmeal. Top with vegetables and herbs, and brush with more olive oil. Sprinkle with sea salt and pepper to taste, and bake for 14 minutes or until crisp and golden.
Breadsticks: Divide dough into 4 pieces; roll each into a (7- x 5-inch) rectangle. Cut each rectangle lengthwise into 5 strips. Pull or roll into long sticks: Starting from the center, press downward and outward while rolling toward the ends. Use as little flour as possible for the easiest rolling. Brush with olive oil, and sprinkle with salt, pepper, and herbs (such as fresh rosemary). Bake at 450° for 13 minutes or until golden brown and crispy.