Boil a large pot of water for pasta, cook according to package directions. Drain and toss with 3 T butter.
In a small saucepan, bring balsamic vinegar to a boil over medium-low heat. Boil, stirring constantly about 5-10 minutes or until balsamic has become the consistency of maple syrup. There should only be about 3-4 T left. Be careful not to burn,.
Meanwhile, place 1 T of butter in a skillet with onions and salt and pepper to taste. Stir fry onions over medium heat until transparent. Add broccoli and mushrooms along with 1/3 cup water. Cook, stirring every now and then for about 5 minutes or until broccoli is tender and water has evaporated.
Mix pasta, balsamic reduction, cooked veggies, raw spinach and cheese together. Serve and garnish with extra pepper and cheese.