1. Preheat oven to 500°F. Place pizza stone on bottom rack of oven; heat for at least 30 minutes.
2. Crust: Meanwhile, pour water into bowl of stand mixer. Add sugar; stir until sugar is dissolved. Sprinkle yeast over top; let stand for 5 to 10 minutes or until foamy. Add 2 cups of the flour and salt; mix using dough hook attachment. Gradually knead in enough of the remaining flour until ball forms. Transfer dough to floured countertop; knead for about 8 minutes, adding flour as needed to make smooth dough.
3. Place dough in greased bowl; cover with tea towel. Let rise in warm spot for about 1 hour or until doubled in bulk. Knead dough briefly; form into ball. Cover with clean tea towel; let rest for 30 minutes.
4. Toppings: Season steak with 1/2 tsp each salt and pepper. Heat 1 tablespoon vegetable oil in large heavy-bottom pan or cast iron skillet set over medium-high heat. Sear steak for 3 to 4 minutes per side or until well browned. Sear fat cap, rocking back and forth, for 1 to 2 minutes or until evenly caramelized. Remove from heat; let rest for 10 minutes. Slice steak into strips. Set aside.
5. Meanwhile, in same skillet set over medium heat, combine remaining vegetable oil, onion, mushrooms, and remaining salt and pepper; cook, stirring frequently, for 8 to 10 minutes or until mushrooms and onion are browned and tender.
6. Form dough into 14-inch round. Spread cornmeal on pizza peel; arrange dough on top.
7. Sprinkle mozzarella cheese evenly over dough. Top with mushroom mixture and blue cheese.
8. Slide pizza onto pizza stone; bake for 13 to 15 minutes or until cooked as desired.
9. Scatter sliced steak over pizza.
10. Top with baby arugula, Parmesan cheese and drizzle of olive oil.
Use store-bought pizza dough if desired.