Sprinkle both sides of the chicken with salt and pepper.
Use a skillet large enough to fit the pasta.
Heat oil over medium high heat. Add chicken and cook for 2 minutes on each side until golden and cooked through. Remove onto plate and rest for 5 minutes, then slice while pasta is cooking.
Add milk, chicken broth and garlic. Bring to simmer then add pasta.
Move pasta around every 30 seconds or so until it is softened (around 3 minutes) so it doesn't stick. Once pasta is softened, reduce heat to medium and stir every couple of minutes.
At about 9 - 10 minutes, the pasta should be almost cooked but there should still be liquid covering the base of the skillet. Add cream and parmesan and mix.
Simmer, stirring occasionally, for ~2 minutes, until sauce is thickened and pasta is cooked. If you cook it too long and the sauce goes gluggy, add a splash of hot tap water - will go back to silky with a few tosses.
Adjust salt and pepper to taste and serve immediately, garnished with freshly grated parmesan and parsley!