Bring 4 liters of water to a boil with 20g of salt. Cook spaghetti for 9-11 minutes until al dente.
Pat chicken breasts dry and season with olive oil, salt, and pepper.
Heat a grill pan or cast-iron skillet over medium-high heat. Grill chicken for 6 minutes per side or until internal temperature reaches 74°C.
Transfer chicken to a cutting board and allow to rest for 5 minutes before slicing into 1cm strips.
In a large sauté pan, melt butter over medium heat. Add minced garlic and sauté for 60 seconds until fragrant but not browned.
Pour in heavy cream and bring to a simmer. Reduce heat to low and simmer for 4-5 minutes until the volume reduces slightly.
Gradually whisk in the Parmesan cheese until the sauce is smooth and emulsified.
Drain the pasta, reserving 60ml of pasta water. Incorporate pasta into the sauce, adding reserved water as needed to reach desired viscosity.
Divide pasta into bowls, top with sliced grilled chicken, and garnish with chopped parsley.