To make the Dough
In a small bowl, dissolve the sugar in the warm water. Sprinkle the yeast over the water and stir until it dissolves. Let the yeast mixture stand for 5 minutes, until a layer of foam forms on the surface. In a large bowl, combine the flour and the salt. Make a well in the center of the flour mixture and pour the olive oil and the yeast mixture. Stir the flour into the wet ingredients, until all the flour is incorporated. If its too dry, add more water. On a lightly floured surface, knead the dough for 15 minutes, until it is smooth and elastic. Shape the dough into a ball and put in a well-oiled bowl. Cover with a moist towel and let rise in a warm place until double in bulk (about 1 1/2 hours).
For the Jambalaya Sauce
In a large saucepan, melt butter over medium heat. Add the onion and bell pepper. Cook, stirring frequently, until vegetables are tender (10 minutes). Add the chicken stock, tomatoes, tomato paste, soy sauce, salt, cayenne pepper, cumin, pepper, and bay leaf. Stir to blend and bring to a boil. Reduce heat and simmer until really thick (30 minutes). Remove bay leaf.
For the Peppers and Onions
In a medium mixing bowl, stir together the barbecue sauce, soy sauce, and olive oil until thoroughly blended. Add pepper and onions to mixture. Grill or broil coated vegetables until evenly browned (4-5 minutes).
In a large nonstick skillet, heat olive oil over medium high heat. Saute sausages until well-cooked (about 10 minutes). Set aside.
One hour before baking the pizzas, start preheating the oven with pizza stones inside at 500 degrees F. Punch the dough down, and divide into 4 equal portions. Roll out each portion into an 6-8 inch flat circle. Distribute the jambalaya sauce, pepper and onion mixture, sausage, and cheese amongst the 4 pizzas. Bake until crust is crispy and cheese is bubbling (8-10 minutes).