Place chickpeas, garlic, cayenne pepper, lemon juice, honey and tahini in the bowl of a food processor and process until smooth. With the machine running, slowly add the olive oil until emulsified. Season with salt and pepper, to taste.
For the pizza:
Heat the grill to high. Brush both sides of the pizzas with oil and season with salt and pepper. Grill until golden brown on both sides, about 2 minutes per side.
Top each pizza with the spicy hummus. Arrange any or all of the veggies on top of the hummus and top with the goat cheese. Season with salt, pepper and ancho powder. Place the bread back on the grill, close the cover and grill for 5 minutes to heat through. Remove and add black olives and fresh basil.
In a large bowl stir together 1/3 cup water, yeast, and sugar and let stand until foamy, about 10 minutes. Stir in remaining 1/3 cup water, 2 tablespoons oil, 1 3/4 cups flour, cornmeal, and salt and blend until the mixture forms a dough. Knead dough on a floured surface, incorporating as much of remaining 1/4 cup flour, as necessary, to prevent dough from sticking, until smooth about 5 to 10 minutes. Form the dough into a ball.
Lightly oil the sides and bottom of a large bowl with oil, add the dough, turn to coat in the oil, cover and let rise in a warm place until doubled in size, about 1 hour. Gently punch the dough down and divide into 4 equal pieces. Roll each piece on a lightly floured surface into a 10-inch circle that is 1/8-inch thick. Brush off excess flour and transfer the dough to a baking sheet, cover each circle of dough with plastic wrap and continue stacking rolled out pieces on top of each other. Wrap well with plastic wrap and refrigerate until ready to grill.