Before you start, put a large pot of well-salted water on to boil for the pasta.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Season the chicken well with salt, add to the pan, and cook until lightly golden. About 3 minutes in total. You don't want it cooked all the way through.
Set the chicken aside and lower the heat to medium-low.
Add the 4 tablespoons of olive oil and the anchovies if using and break them up with a wooden spoon until mostly dissolved, about 1 minute.
Add the garlic and cook gently until softened and fragrant, about 30 seconds. The garlic should not brown, adjust the heat as needed.
Add the red pepper flakes and tomato paste and cook for 1 minute.
Add the tomatoes (as I said in the notes I like to blitz them to a puree before adding, it creates a smoother, richer sauce), bring to a very gentle simmer.
Add the sugar and a couple of big pinches of salt and the basil springs.
Bring the sauce to a very gentle simmer and cook for 15 minutes to let the flavors develop. It can simmer a little longer if needed, but make sure the chicken is only added for the final 8 minutes so it cooks through but stays juicy.
While the sauce simmers, cook the pasta until just shy of al dente (I usually undercook by a minute from package instructions)
Remove the basil from the sauce and add your cooked pasta in with a little splash of pasta water and let it gently bubble away together for 1 - 2 minutes.
An optional step is to add 2 tablespoons of butter for a bit of gloss. Check for seasoning and serve with some fresh torn basil leaves and as much freshly grated Parmesan as your heart desires.