Combine 1 cup flour, undissolved yeast and salt in a large bowl. Heat water and olive oil until very warm (120° to 130°F). Gradually add to flour mixture and beat 2 minutes at medium speed. Add enough remaining flour to make a soft dough. Knead until smooth and elastic, about 8 to 10 minutes. (If using RapidRise Yeast, let pizza dough rest at this point for 10 minutes.)
Roll pizza dough to 12-inch circle; place on pizza pan brushed with olive oil. Form a rim by pinching the edge of the dough; prick surface with fork. Let rest 10 minutes.
Prepare mushroom topping, while dough rests. Heat olive oil in a skillet over medium high heat. Add mushrooms and onion; cook 5 minutes, stirring occasionally. Remove from heat and drain well.
Bake crust in preheated 450°F oven for 10 minutes. Spread with mushroom topping; drizzle with beaten eggs combined with Dijon mustard, salt and pepper. Sprinkle with cheese and bacon. Reduce oven to 375°F and bake for 20 minutes or until eggs are set. Garnish with snipped parsley or basil leaves if desired. Serve immediately.