Bring a pot of salted water to a boil and cook the pasta according to package directions, adding the broccoli florets during the last 2 minutes of cooking.
Reserve 2 tablespoons of the pasta cooking water, then drain the pasta and broccoli.
While pasta cooks, heat the olive oil in a large skillet over medium-high heat and add the cubed chicken breast.
Season the chicken with sea salt and black pepper, sautéing until golden brown and cooked through, approximately 6-8 minutes.
Reduce the heat to low, add the minced garlic to the skillet, and cook for 1 minute until fragrant.
In a small bowl, whisk together the Greek yogurt, parmesan cheese, and reserved pasta water until smooth.
Add the cooked pasta, broccoli, and yogurt mixture to the skillet with the chicken, tossing gently over low heat until the sauce is velvety and coats every piece.