In a small bowl, dissolve the yeast and honey in ¼ cup of the warm water. In a mixer fitted with a dough hook, combine the flour and the salt. Add the oil, yeast mixture, and the remaining ¾ cup of water and mix on low speed until the dough comes cleanly away from the sides of the bowl and clusters around the dough hook, about 5 minutes.
The pizza dough can also be made in a food processor. Dissolve the yeast as above. Combine the flour and salt in the bowl of a food processor fitted with the steel blade. Pulse once or twice, add the remaining ingredients, and process until the dough begins to form a ball.
Turn the dough out onto a clean work surface and knead by hand for 2-3 minutes. The dough should be smooth and firm. Cover the dough with a clean, damp towel and let it rise in a warm spot for about 30 minutes. When ready, the dough will stretch as it is lightly pulled.
Place a pizza stone on the middle rack of the oven and preheat the oven to 500 degrees. Divide the dough into 4 balls, about 6 ounces each. Work each ball by pulling down the sides and tucking under the bottom of the ball. Repeat 4-5 times. Then on a smooth, un-floured surface, roll the ball under the palm of your hand until the top of the dough is smooth and firm, about 1 minute. Cover the dough with a damp towel and let it rest for 15-20 minutes. At this point, the balls can be wrapped in plastic and refrigerated for up to 2 days.
To prepare each pizza, dip the ball of dough into flour, shake off the excess flour, place the dough on a clean, lightly floured surface, and start to stretch the dough. Press down on the center, spreading the dough into an 8-inch circle, with the outer border a little thicker than the inner circle. If you find this difficult to do, use a small rolling pin to roll out the dough. Lightly brush the inner circle of the dough with oil and arrange the toppings of your choice over the inner circle.
Using a lightly floured baker’s peel or a rimless flat baking tray, slide the pizza onto the baking stone and bake until the pizza crust is nicely browned, 10-12 minutes. Remember that the oven is very hot and be careful as you place the pizza into and out of the oven. Transfer the pizza to a firm surface and cut into slices with a pizza cutter or very sharp knife. Serve immediately.