Bring a large pot of salted water to a boil and cook the whole wheat penne according to package directions.
Add the broccoli florets to the pasta water during the final 3 minutes of cooking, then drain, reserving 0.25 cup of the starchy pasta water.
While pasta cooks, season the chicken breast with sea salt, black pepper, and dried oregano.
Heat olive oil in a large skillet over medium-high heat and sauté the chicken until golden brown and cooked through, about 5-6 minutes per side.
Lower the skillet heat to medium-low, add the minced garlic, and cook for 1 minute until fragrant.
In a small bowl, whisk the Greek yogurt, parmesan cheese, and reserved pasta water until smooth to create the sauce.
Add the cooked pasta, broccoli, and yogurt sauce to the skillet with the chicken, tossing gently until everything is coated and creamy.