Prepare the ingredients as instructed above.
Bring a pot of water to a boil. Add salt to the water and cook broccoli until tender. Drain well and set aside.
Season the chicken with salt and pepper and drizzle with olive oil.
Heat a grill or grill pan over medium heat. Grill the chicken on both sides until it reaches an internal temperature of 165°F (74°C). Set aside.
In a pan over medium heat, add in heavy cream and simmer until creamy. Add half of the Parmesan cheese and whisk until smooth.
In a separate pot, bring water to a boil. Salt the water and cook the fettuccine pasta according to package instructions.
Drain the pasta, reserving 1/2 cup of the pasta water.
Add pasta, grilled chicken, and broccoli to the Alfredo sauce. Toss to coat. Add reserved pasta water as needed for creaminess. Garnish with remaining Parmesan.
Prepare the Salad: In a bowl, combine the cucumber, tomato, red onion, extra virgin olive oil, red wine vinegar, salt, and black pepper, oregano. Toss gently to combine.
Pour sparkling water over lemon. Serve with ice if desired.
Serve the fettuccine Alfredo with Greek salad and lemon sparkling water.