I pat the chicken breasts dry, then season both sides generously with salt and pepper. In a hot skillet with olive oil, I sear each side for about 6 to 7 minutes until golden and cooked through. Once done, I let it rest for a few minutes before slicing it into thin strips.
While the chicken rests, I bring a large pot of salted water to a boil. I cook the fettuccine until just al dente, following the package timing. I always save a splash of pasta water before draining, just in case the sauce needs loosening later.
In the same skillet used for the chicken, I melt the butter over medium heat and toss in the minced garlic. I let it cook for about a minute, just until it turns fragrant, stirring constantly so it doesn't burn.
I pour in the heavy cream slowly, stirring as I go. I let the mixture simmer gently for 2 to 3 minutes, watching it thicken slightly. This step is where the sauce really starts to look like real alfredo.
I lower the heat and whisk in the freshly grated Parmesan a little at a time. This keeps the cheese from clumping and gives me that smooth, glossy texture I'm after. I season with salt and pepper here too.
I add the drained pasta and sliced chicken straight into the skillet with the sauce. I toss it all gently until every strand of pasta is coated and the chicken is warmed through evenly.
I take the skillet off the heat and let it sit for a couple of minutes. This lets the sauce settle and cling to the pasta better before I plate it up.