Preheat grill on high heat or oven to 500 degrees. Pre-heat pizza stone for 30 minutes before cooking pizza.
Cook onion in 1-2 T of olive oil over medium low heat for 20 minutes or until caramelized. Add salt, pepper, fresh thyme and set aside. In a separate pan, cook ground beef in 1 T olive oil over medium heat for 3 minutes with 1 crushed garlic clove and salt and pepper to taste. Continue cooking until browned. Drain off grease and set aside in bowl. Char pepper over open flame and place in plastic bag for 5 minutes to loosen skin, then peel and slice thinly.
Flour or corn meal the pan or pizza stone to ensure crust doesn’t stick. Brush 1 T of olive oil and one crushed garlic clove over crust. Add shredded cheese evenly, ground beef, onions and peppers. Bake on hot pizza stone until cheese is melted and sides are crispy brown, about 4-8 minutes. Serve pizza garnished with fresh arugula and a drizzle of olive oil. Serves 3-4.