In a small bowl, dissolve the yeast and honey in 1/4 cup of the water.
In an electric mixer fitted with a dough hook, combine flour and salt. Add oil, yeast mixture, and remaining 3/4 cup of water, and mix on low speed until the dough comes cleanly away from the sides of the bowl and clusters around the hook, about 5 minutes. (Or use a food processor fitted with the steel blade: Pulse flour and salt, add remaining ingredients, and process until dough begins to form a ball.)
Turn dough onto a clean work surface, and knead by hand for 2 or 3 minutes until smooth and firm. Cover with a damp towel, and let rise in a warm spot for about 30 minutes. When ready, dough will stretch if lightly pulled.
Divide the dough into four 6-ounce balls. Work each ball by pulling down the dough on the sides and tucking it under the bottom. Repeat 4 or 5 times. On a smooth, unfloured surface, roll the ball under the palm of your hand for about 1 minute. Cover dough with a damp towel, and let rest 15 to 20 minutes. Wrap half of dough (2 balls) in plastic and store in the refrigerator for up to two days.
Place a pizza stone on the middle oven rack, and preheat to 500 degree F.
On a lightly floured surface, stretch or roll out 2 balls of dough into one 10-inch round or two 8-inch rounds. Brush lightly with pesto, and scatter dried tomatoes evenly. Sprinkle on mozzarella and fontina, then arrange Roma tomatoes. Sprinkle with goat cheese, oregano, thyme, and Parmesan. Bake until crust is nicely browned, 10 to 12 minutes.
Transfer pizza(s) to a cutting board; garnish with basil. Cut and serve immediately.