Preheat oven to 425ºF. On a small baking pan, add the poblano pepper, garlic and serrano pepper. Roast for 30 minutes, turning after 15 minutes. Remove from oven and let cool.
Combine all of the ingredients in the blender, adding about 1 teaspoon of salt. Blend on high until smooth. If you have trouble getting it to blend, add a little more olive oil. Taste for salt. Great sauce for Mexican style pizza or as a chile pesto for pasta.
In a medium skillet, heat 2 tablespoons of olive oil to medium heat. Add the onions and cook for 4 to 5 minutes; add the garlic and cook for 1 more minute. Remove from pan, onto plate and set aside. In that same pan, add another tablespoon of olive oil. Heat to medium heat, add the sliced chayote and season with salt and pepper. Cook for a few minutes, until it starts to brown. Remove from heat and set aside.
Preheat the oven to 475ºF.
On a lightly floured surface, roll out the dough as much as you can. Take some olive oil and drizzle it on a sheet pan, sprinkle some cornmeal onto the pan, lay the dough on top and, using your hands, work the dough and shape it, pressing down firmly. Drizzle with olive oil then add mozzarella, poblano sauce, onions, garlic, chayote squash, olives, cilantro, crushed jalapeño, oregano, Parmesan cheese, olive oil (making sure you drizzle the exposed crust also) and fresh cracked pepper.
Bake for 11 to 13 minutes. Remove from oven, and let cool slightly before cutting pizza.