Boil fettuccine in salted water until al dente. Reserve 1 cup pasta water, then drain.

Season chicken with salt and pepper. In a large skillet over medium-high, heat olive oil and sear chicken in a single layer until golden and cooked through, about 3 to 4 minutes per side. Transfer to a plate.

Melt butter in the same skillet over medium heat. Add garlic and cook 30 seconds. Add broccoli and cook, stirring occasionally, 2 to 3 minutes until bright green and tender-crisp.

Pour in heavy cream and bring to a gentle simmer. Reduce heat to low, then stir in parmesan a little at a time until melted and sauce thickens slightly, 3 to 4 minutes.

Return chicken to the skillet, add drained fettuccine, and toss to coat. Add reserved pasta water a tablespoon at a time if needed to loosen the sauce. Garnish with parsley and serve.