Bring a large pot of salted water to a boil and cook the linguine according to package instructions. Make sure it’s al dente, as it will finish cooking in the sauce.
Before draining, reserve about ½ cup of pasta water to help adjust the sauce later if needed. Drain and set aside.
Heat olive oil in a large skillet over medium heat. Season the sliced chicken with salt and pepper before adding it to the pan.
Cook until golden brown and fully cooked through, about 5–7 minutes. Remove the chicken from the pan and set aside.
In the same skillet, melt the butter over medium heat. Add the minced garlic and sauté for about 30 seconds until fragrant but not browned.
Pour in the heavy cream and bring it to a gentle simmer. Let it cook for 3–4 minutes, stirring occasionally, until slightly thickened.
Reduce the heat to low and gradually stir in the freshly grated Parmesan cheese. Stir continuously to prevent clumping.
Add nutmeg if using, and adjust seasoning with salt and pepper. The sauce should be smooth and creamy.
Return the cooked chicken to the skillet. Add the drained linguine and toss everything together until well coated.
If the sauce feels too thick, add a splash of reserved pasta water to loosen it. Finish with chopped parsley before serving.