Melt 3 tbsp butter and 1 tsp sugar in a heavy bottomed skillet over medium high heat. Add onions and sauteed until golden colored, stirring every couple of minutes.
Move onions to the side of the pan, reduce heat to medium, and add mushrooms and garlic. Saute until mushrooms are beginning to brown. Remove onion, mushroom and garlic mixture from pan and set aside.
Meanwhile, fill stockpot with water and 2 tbsp salt and let it come to a boil.
Once water is boiling, add spaghetti and cook until al dente. Reserve a ladle full of pasta water for sauce. Drain pasta in colander.
Add 1/2 tbsp oil to pan and saute prepared chicken cutlets until cooked through and lightly browned. Remove chicken to same plate as onion and mushroom mixture. .
While pan is still hot, add wine and let the alcohol cook down, approximately 3 minutes. Scrape up the pan bits with a spatula.
Reduce heat to just above medium low and add the cream, basil, tomatoes, reserved water, as well as salt and pepper to taste. Simmer, but do not let boil.
Add the chicken, mushrooms, and onions back into sauce mixture. Lightly stir to incorporate.
Serve over cooked pasta. Garnish with basil and grated Parmesean cheese.