Pat your 2 chicken breasts dry with paper towels and sprinkle both sides with salt and pepper. Heat the olive oil in a large skillet over medium-high heat until it shimmers—you'll hear it sizzle when the chicken hits the pan. Sear the chicken for 6-7 minutes per side until golden brown, then set it aside on a plate (it won't be cooked through yet, and that's fine).
In the same skillet, melt the butter over medium heat and add your diced onion. Cook for about 3 minutes until it starts getting soft and a little golden. Add the minced garlic and cook for 1 more minute—you'll smell that amazing garlic aroma when you know it's ready.
Pour in the chicken broth and use a wooden spoon to scrape up all those brown bits stuck to the pan (that's flavor, don't skip it). Bring everything to a simmer and then carefully nestle the seared chicken breasts back into the skillet. Reduce heat to medium and simmer for 12-15 minutes until the chicken reaches 165°F internally.
Remove the cooked chicken to a cutting board and let it rest for a few minutes. Meanwhile, keep the broth simmering in the skillet—don't turn off the heat yet. Slice the chicken into bite-sized pieces (I go about 3/4-inch thick) and set aside for a moment.
Pour the whole milk and heavy cream into the simmering broth, stirring constantly to combine everything smoothly. Keep the heat at medium and watch closely for the next few minutes—you want steam rising but no aggressive boiling. When it starts to bubble gently around the edges, it's time for the cheese.
Reduce heat to medium-low and sprinkle in the grated Parmesan cheese a handful at a time, stirring constantly after each addition. This is the part where patience actually matters—I learned this the hard way because I dumped it all in once and ended up with clumpy disaster. Add the nutmeg and give everything a taste, then adjust salt and pepper if needed.
Meanwhile, cook your fettuccine according to package directions (usually 8-10 minutes) and drain it well. Toss the pasta into the creamy sauce along with the sliced chicken and stir gently to coat everything. Cook for just 1-2 minutes more to let the flavors meld together before serving hot.