To prepare topping, heat 1 teaspoon olive oil in a heavy medium skillet over medium heat. Cook sausage in hot oil 5 minutes or until browned; stir to crumble. Add bell pepper, mushrooms, and onion; cook 4 minutes or until vegetables are tender, stirring occasionally. Add garlic; sauté 1 minute. Stir in olives; drain sausage mixture on paper towels.
To prepare crust, dissolve yeast and 1/2 teaspoon sugar in warm soy milk in a small bowl; let stand 5 minutes.
Weigh or lightly spoon 3 ounces brown rice flour (3/4 cup) into dry measuring cups; level with a knife. Place brown rice flour, remaining 2 teaspoons sugar, cornstarch, and next 3 ingredients in a food processor. With processor on, pour yeast mixture, 1 tablespoon olive oil, and vinegar through food chute; process 30 seconds, adding 2 tablespoons brown rice flour, 1 tablespoon at a time if necessary, until mixture forms a ball.
Coat a 12-inch pizza pan with cooking spray. Place dough on pan; dust with remaining 2 tablespoons brown rice flour to prevent sticking to fingers. Press dough onto pan; crimp edges of dough with fingers to form a rim. Place on bottom rack of oven.
Bake at 450° for 10 minutes. Remove from oven, and brush edges of crust with remaining 1 teaspoon olive oil. Spread pizza sauce evenly over crust. Top with sausage mixture and cheese. Place on middle rack of oven. Bake at 450° for 15 minutes. Cool pizza in pan on a wire rack 5 minutes. Cut into 6 wedges.
Cooking Tip Xanthan gum is a corn-based product often used in gluten-free baking as a substitute for wheat gluten to thicken and bind. Using too much can result in a baked good that is heavy or gummy, so be sure to measure carefully. Most recipes call for 1 to 2 teaspoons—a little can go a long way.