Begin by making the pizza dough: Add the water, one tablespoon of oil, flour, honey, salt, and yeast in the order suggested by your bread machine. Select the dough cycle, and press start.
While the dough rises, make the pomodoro and pesto sauces. For the pomodoro sauce: In a three quart saucepan, half filled with boiling water, simmer the tomatoes for three minutes, or until their skins have loosened. Drain and peel the tomatoes, and chop them up.
In a large Dutch oven, heat the butter and oil and cook the onion and garlic until they're soft. Add the tomatoes, wine, bay leaf, chicken stock, basil, sugar, and a half teaspoon of kosher salt.
For the Pesto Sauce: In a food processor, place the basil, garlic, Parmesan, pine nuts, and a quarter teaspoon each of kosher salt and black pepper. Process until they're all ground up. Then, with the motor running, drizzle in a third a cup of oil.
Preheat the oven at 425 degrees, and heat the pizza stones for thirty minutes.
Place parchment paper on the pizza peels, and using your fingers press each ball of dough into a twelve inch circle. Brush each circle with olive oil, and cover loosely with plastic wrap. Let rise for thirty minutes. Then bake for 15 minutes.
Remove the pizza from the oven, and spread the pomodoro sauce on each pizza. Add the cheese and then the sliced tomatoes. Bake for five more minutes, or until the cheese melts, and then drizzle with pesto.