Bring a large pot of salted water to a boil and cook the whole wheat penne according to package directions until al dente.
During the last 3 minutes of pasta cooking, add the broccoli florets to the boiling water to blanch them.
Reserve 0.25 cup of the starchy pasta water, then drain the pasta and broccoli.
While pasta cooks, season the chicken breast with sea salt and black pepper.
Heat olive oil in a large skillet over medium-high heat and cook the chicken until golden brown and cooked through, about 5-7 minutes per side.
Remove chicken from the skillet, let it rest for 2 minutes, then slice into strips.
In the same skillet, reduce heat to low and sauté the minced garlic for 1 minute until fragrant.
Whisk together the Greek yogurt, parmesan cheese, and the reserved pasta water in a small bowl until smooth.
Add the pasta, broccoli, and chicken back into the skillet and pour the yogurt mixture over the top.
Toss everything gently over low heat until the sauce is creamy and coats the pasta evenly.
Garnish with fresh chopped parsley and serve immediately.