To Make Dough: Dissolve yeast in warm water and set aside. Combine flour and salt in mixing bowl. Make a well in the center of flour. Add the yeast mixture, oil and 3/4 cup of water. Stir and mix with a wooden spoon until a rough ball of dough is formed and dough cleans the sides of bowl. Turn dough out of bowl onto a lightly floured work surface. Knead dough for 7 to 8 minutes until it is smooth and satiny (dust dough with flour if it feels sticky). Dust a large mixing bowl lightly with flour. Place dough in bowl; cover with plastic wrap and a kitchen towel. Put dough in a warm place to rise for 1 1/2 hours, until double in bulk.
After dough has doubled in bulk, punch down and turn out of bowl onto work surface. Knead lightly for about 2 minutes. Roll or stretch dough into a circle that is 16 inches in diameter and about 1/4-inch thick. Place dough in a 16-inch flat pizza pan. Cover dough with a clean towel and let rise a second time for about 45 minutes before adding toppings.
To Make Barbecue Sauce: Combine all barbecue sauce ingredients in a 2-quart saucepan. Bring to a boil. Turn heat down and simmer for 20 minutes, stirring frequently. Remove pan from heat. Strain out cloves and onions. Let cool to room temperature. Refrigerate until ready to use. Sauce can be made 1 or 2 days ahead. Makes 2 cups of sauce.
To Assemble Pizza: Preheat the oven to 500 degrees F.
Spread 1/3 of barbecue sauce evenly over dough to within 1/2 inch of edge. Mix the mozzarella and cheddar cheese and sprinkle them over the sauce. Bake pizza for about 10 minutes until crust is golden brown and cheese is bubbly. Remove pizza from oven and spread barbecue meat over the cheese. Add remaining barbecue sauce evenly over meat. Serve at once.