Put the tablespoon of olive oil in a cold skillet large enough to fit the cooked pasta in at end and add the sliced garlic.
Bring to a gentle sizzle over a medium heat then cook for 30 seconds or so, moving it around so it doesn't brown. Cooking it from cold might seem strange but it helps to infuse the oil with the garlic flavor.
Lower the heat slightly and add the wine, it will bubble up a lot.
Cook so it is gently simmering for about 4 mins, you are wanting to reduce it down roughly by half.
Add the butter pieces in, one at a time, letting each piece melt and whisking well in between each addition. A flat whisk is brilliant for this.
You should end up with a very yellow and slightly thickened sauce at the end. Try and time the pasta cooking so you can add the pasta straight in to butter sauce at this stage. You can take the sauce off the heat if you need to though.
Add a ¼ cup reserved pasta water and whisk vigorously. I like to whisk and shake the pan at the same time to get a nice emulsified sauce.
Add the black pepper and mix through.
Add the cooked pasta straight in and toss with the sauce using tongs. Arrange the pasta in a nice level layer, spreading it out.
Turn the heat down to low and sprinkle the parmesan over the top of the pasta in an even layer.
Leave it alone until it is melting on top, about 1 min, then take some tongs and spin the pasta around and around until you get a lovely glossy sauce. Check out video below to see this in action!
Taste for seasoning and add salt if you need. Add the parsley and mix through.
Serve straight away, top with the sliced chicken and some extra parmesan.