Prepare all ingredients as listed above.
Bring a pot of water to a boil. Add salt to season the water. Cook broccoli until tender, then drain well and set aside.
Season chicken with salt and pepper, then drizzle with olive oil.
Heat a grill or grill pan over medium heat. Grill the chicken on both sides until cooked through to an internal temperature of 165°F (74°C). Set aside.
Add the heavy cream to a pan over medium heat, bring to a simmer and let it reduce until creamy. Remove from the heat. Add half of the Parmesan cheese to the cream mixture and whisk until smooth.
Bring another pot of water to a boil. Add salt to season the water. Cook pasta according to package instructions until al dente.
Drain the pasta, reserving about 1/2 cup of the pasta water.
Add pasta, grilled chicken, and broccoli to the Alfredo sauce. Toss to coat evenly.
Garnish with the remaining Parmesan cheese. Add reserved pasta water as needed for a smooth, creamy consistency. Finish with chopped parsley.
Arrange tomato and avocado slices on a serving plate. Drizzle with olive oil, sprinkle with diced garlic, and season with salt.
Combine pineapple juice, water, sugar, and lime juice. Stir until sugar is dissolved. Add ice if desired. Garnish with lime slices and fresh mint.
Serve the fettuccine Alfredo with tomato-avocado salad and pineapple agua fresca.