In a food processor or mixer with a dough hook, combine the yeast, sugar and 3/4 cup water. Allow the yeast to proof for about 5 minutes, (bubbles will form around the outer edges).
Add the oil, flour, and salt. Begin processing or mixing the ingredients, slowly pouring in the remaining 1 cup of water. Mix until the dough balls together and is shiny and elastic, about 5 minutes. Add a little olive oil to a large bowl and spread evenly around the bowl to prevent the dough from sticking. Add the dough, cover with plastic wrap and put in a warm spot (I use the microwave oven) for about 2 hours. Punch the dough down and let it rise again, about another 2 hours. I prefer to make my dough early in the day for evening dinner or a day ahead.
Combine all the ingredients in a small saucepan and simmer over medium-low heat until the sauce is slightly thickened, about 30 minutes.
I use 2 ovens when I cook my pizzas, 1 oven is preheated to 450 degrees F with a Hearth-kit in it, and the other oven is preheated at 500 degrees F with a pizza stone. Heat the stones for at least 1 hour before baking pizzas.
Divide the dough into 4 equal portions. Roll out dough until very thin and cannot be rolled further. Sprinkle about 1/2 teaspoon of polenta onto a pizza peel. Put the dough on the peel and spread 1/2 tablespoon of oil all around the edges. Add 1/4 cup of pizza sauce to the middle of the dough and spread it to the outer edges, leaving about a 1-inch margin. Sprinkle the sauce with the mozzarella and Monterey Jack cheeses. Top with crumbled sausage and drizzle the remaining 1/2 tablespoon of olive oil over the pizza. Bake for 10 minutes in the 450 degree F oven. (If using only 1 oven, raise the heat to 500 degrees F.) Remove the pizza from the oven and top with the cooked crawfish. Put the pizza in the 500 degree F oven and cook until the top is golden brown and bubbling, about 2 minutes.
Transfer the pizzas to a cutting board and slice. Arrange on a serving platter and serve.
Mangia, mangia .
Cook's Note: The dough recipe will make 2 pizzas, the topping recipe will make 1 pizza, each pizza will feed 2 people.
A viewer, who may not be a professional cook, provided this recipe. The Food Network Kitchens chefs cannot make representation as to the results.