Preheat your oven to 500 degrees F or as hot as your oven goes (the max might be 450 F and that works, too).
In a measuring cup, measure out the lukewarm water and then mix in the active dry yeast and honey. Let stand 5 minutes. Meanwhile, in the bowl of a stand-up mixer, with the hook attachment (you can also do this by hand but I’m super lazy), add the all-purpose flour and salt. Give it a mix. When the yeast and water mixture is nice and foamy, pour it into the flour mixture and turn the mixer on low. At first the dough will be shaggy and dry, but eventually it’ll all come together. Keep the mixer on for about 5 minutes, during this time a ball of dough will form. Stop the mixer and pull the dough off the hook. Form it into a round ball and then halve the dough; form it into two balls. Allow it to rise on the counter, uncovered, for about 10 to 15 minutes. During this time, let’s get the toppings ready.
Sprinkle the cornmeal or masa on a pizza peel. If you don’t have one, like me, flip over a (clean) baking sheet and dust that with cornmeal or masa. To form the pizza, start flattening the dough using your fingers, don’t be afraid to pull the dough, thinning it out. I also like to pick up the dough and stretch it in the air a bit, allowing gravity to assist in the process. Flatten it out onto the pizza peel or baking sheet. Repeat with the second ball.
Divide the tomato sauce amongst pizza doughs. I personally favor a super thin layer. Set a handful or two of cheese aside (we’re gonna put this on toward the end). Sprinkle the remaining cheese atop the pizza sauce. Next, arrange the summer squash, okra, tomatoes and shishito peppers. Slide it onto your pizza stone or pizza steel and cook for about 10 minutes, rotating the pizzas every so often if needed. At the 10 minute mark, sprinkle the reserved cheese all over the pizza. The oven will be too hot to sprinkle it on just the right spots so just throw it on--WHATEVER! Bake for an additional 1 to 2 minutes.
Carefully remove the pizza from the oven (I found a fork and pancake spatula to be great tools!). Top each pizza with a drizzling of olive oil, a few fresh basil leaves, a sprinkling of crushed red pepper and some parmesan shavings. Cut and serve, piping hot.