Heat a large pot of water over high heat until boiling. Salt the water to your preference and add the pasta. Cook until just shy of al dente (the pasta will finish cooking in the sauce later). Save 1 cup of the pasta water. Drain the pasta and set aside.
Prepare the Chicken
While the water is heating, start your chicken. Heat a large frying pan over medium heat. Add 2 Tablespoons of oil
While heating, put the flour in a shallow dish with a pinch of salt. Coat each chicken piece on all sides in the flour, shaking to remove excess flour.
When the pan and oil are hot, cook the chicken until just golden brown on each side, approximately 5-7 minutes per side. Repeat with all chicken, adding more oil as needed. Set the chicken aside.
Make the Scampi Sauce
As you are working on batches of chicken, make your sauce. Heat a medium saucepan over medium heat. Add 2 Tablespoons of butter until melted.
Add the onion and garlic to the butter and cook until just soft but not brown, approximately 3 minutes.
Add the white wine and simmer to burn off some of the alcohol and reduce 2 minutes. Scrape up any bits from the bottom of the pot while simmering.
Add the chicken stock, lemon juice, parsley, and crushed red pepper. Simmer 5 minutes.
Remove the sauce from the heat and whisk in the remaining 8 Tablespoons (1/4 stick) of butter until incorporated. Set aside.
Vegetables and Assembly
Put the large pot from the pasta back on the stove (or a new large pot - but one less thing to clean!). Add 1 Tablespoon of oil and heat over medium heat.
Once hot, add the peppers and onion and cook until just beginning to soften, approximately 3-5 minutes.
Add the pasta and sauce to the pot. Gently toss to coat and combine (be very gentle to help prevent the pasta from breaking - once the pasta meets the warm sauce, it will start to loosen up and unstick). Season to taste with salt and pepper. Use the pasta water if needed to loosen the sauce and make it saucier as desired.
Serve the pasta in one large dish or as individual portions. Place the pieces of chicken on top.
There are a lot of parts to this recipe, but many of them can be done at the same time. You can also make the chicken and/or sauce in advance for an even easier meal.