Slice onions thinly (aiming for rings that can be rendered down)
Heat 1 tablespoon of olive oild on medium-high heat in a skillet. Add sliced onions. Cook for 10 minutes stirring frequently so they do not burn.
As onions start to brown after the first 10 minutes, reduce to medium heat, and cook for an additional 10 minutes. Still stirring frequently. After reducing heat, add salt to taste (about 1 tbsp.)
(Now at 20 minute mark) Reduce heat further to medium/low. Stir occasionaly for 10 more minutes. At the end of this they should be carmelized and have cooked for 30 minutes total.
Begin to boil water for pasta, and add pasta as the water boils. Cook according to packaging (Farfalle tends to be 8-14 minutes)
Remove skillet from heat, sprinkle onions with balsamic vinegar to deglaze pan. Use spatula to scrape the bottom of the pan to deglaze with vinegar. Remove onions from pan and set aside.
Heat 1 tbsp. olive oil in same skillet as onions were cooked in. Add mushrooms, sprinkle with salt.
Cook mushrooms for about 5 minutes, stirring occassionally until mushrooms are soft.
Add fresh spinach to skillet and stir on low or until spinach starts to wilt.
Add half-and-half mixture to the mushroom and spinach mixture. Raise heat to bring to a quick boil.
Immediately after it begins to boil, reduce to a simmer.(If using elextric stove top, you may have to remove from heat for a moment.)
Add shredded parmesan cheeseand salt to taste. Keep stirring while the sauce simmers and until cheese melts
Add carmelized ions back to the skillet with the pasta sauce (Sauce, mushrooms, spinach, now adding onions)
At this point, pasta should be done, remove and drain the pasta. If the sauce is too thick, add a little of the pasta water to the sauce. Immediately add pasta into sauce, serve.