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: Heat vegetable oil in large skillet set over medium-high heat; cook chicken and 1/2 teaspoon each salt and pepper. Cook for 8 to 10 minutes, turning occasionally until well browned all over. Transfer to plate; set aside.
5. Heat remaining oil in same skillet set over medium heat; cook onion, garlic and ginger for 3 to 5 minutes or until softened. Add garam masala, turmeric, cinnamon and chili powder; cook for about 1 minute or until very fragrant. Return chicken to skillet; stir until well coated. Add tomato paste; cook for 1 minute. Stir in crushed tomatoes; reduce heat to medium-low. Stir in cream; simmer for 12 to 15 minutes or until thickened and chicken is cooked through. Stir in butter; season with remaining salt and pepper.
6. Form dough into 14-inch round. Spread cornmeal on pizza peel; arrange dough on top.
7. Sprinkle 1 cup mozzarella and Cheddar cheese evenly over dough. Top with 2 1/2 cups of the chicken mixture. Top with red onion and remaining mozzarella cheese.
8. Slide pizza onto pizza stone; bake for 13 to 15 minutes or until cooked as desired.
9. Top with drizzle of yogurt and sprinkle of cilantro leaves.
Use store-bought butter chicken sauce and cooked rotisserie chicken for quick preparation.
Leftover butter chicken can refrigerated for up to 3 days and served with steamed hot rice or pita bread.
Use store-bought pizza dough, if desired.
The dough can be prepared the day before and proofed overnight in the fridge if desired.