Place a medium sized pan on medium/high heat for two minutes. Season chicken breasts on both sides with salt and pepper.
Add enough olive oil to thoroughly coat the bottom of pan. Wait 1 minute, allowing oil to get hot. Place breasts in pan and sear for five minutes, flip chicken, add one cup of water to pan, cover with lid, and cook for 3-4 more minutes. Turn off heat and allow to cook in the hot pan for 15 more minutes with lid on. Do not lift lid! The heat needs to stay in the pan for the chicken to cook through.
Peel and slice onion, chop parsley, grate cheese, chop garlic , chop walnuts and set aside
In a separate LARGE pan (pan needs to be big enough to fit cooked pasta:
Place a 1-2 tablespoons of oil in pan. Heat on medium heat. When oil shimmers, add onions. Stir occasionally for about 15 minutes (the key to caramelized onions is patience, keep the heat at medium and resist the temptation to cook them faster)
When onions have reduced in size by half, remove from heat and drizzle with balsamic vinegar and add garlic.Stir and set aside.
When chicken and pasta are done, save a 1/4 cup pasta water and strain pasta (do not rinse) place in pan with onions, add 1-2 tablespoons olive oil, toss with herbs, nuts and arugula. Season with sea salt and pepper, toss again. If needed drizzle in ome of that pasta water, you may or may not need it.
To plate: divide pasta onto four plates. Slice chicken breasts on the diagonal and place on top of pasta
Sprinkle with parsley, parmesan and pomegranate seeds.. Serve.