Heat butter and olive oil in a large skillet over medium heat. Add onion. Sauté until onions are caramelized and soft, about 10-15 minutes. Add mushrooms and more butter and oil if needed. Sauté an additional 5 minutes.
Spread Kale and Arugula Pesto over pizza crust top with cheeses, caramelized onions, mushrooms and tomatoes.
Bake 10-12 minutes until the cheese melts and bubbles.
Sprinkle arugula and crushed red pepper to taste over pizza. Cut and serve hot.