Bring a large pot of water to a boil and cook the brown rice pasta until al dente, about 8-10 minutes.
Reserve 2 tablespoons of the starchy cooking water, then drain the pasta and set it aside.
Season the chicken breast with sea salt and black pepper on both sides.
Heat olive oil in a skillet over medium heat and cook the chicken until browned and the internal temperature reaches 165°F.
Remove chicken from the pan, let it rest, then slice it into thin strips.
In the same skillet, add the broccoli florets and minced garlic, sautéing for 3 minutes until the broccoli is bright and tender.
In a small mixing bowl, whisk together the Greek yogurt, parmesan cheese, and reserved pasta water until smooth.
Return the sliced chicken and cooked pasta to the skillet with the broccoli.
Turn the heat to low and pour in the yogurt mixture, tossing everything together until the sauce is creamy and coats the pasta.
Serve immediately topped with fresh chopped parsley.