Dredge chicken strips in flour mixed with salt and pepper. Heat olive oil in a large skillet over medium-high heat, then sear chicken 4 minutes per side until golden and cooked through. Transfer to a plate and tent with foil.

Cook fettuccine in salted boiling water until al dente. Reserve 1/2 cup pasta water, then drain and set aside.

Melt butter in the same skillet over medium heat. Add garlic and cook 1 minute. Pour in heavy cream, simmer 2 to 3 minutes, then whisk in Parmesan a handful at a time until smooth.

Toss drained pasta in the sauce, using reserved pasta water as needed to loosen. Slice the chicken, place it on top, and serve immediately with extra Parmesan.