Bring a pot of salted water to a boil and cook the brown rice penne according to package instructions until al dente.
While the pasta cooks, season the chicken breast with sea salt, black pepper, and dried oregano.
Heat the olive oil in a large skillet over medium-high heat and cook the chicken until golden brown and cooked through, about 6-7 minutes per side.
Remove the chicken from the skillet to rest, then slice into thin strips.
In the same skillet, add the minced garlic and sauté for 1 minute until fragrant.
Whisk in the chicken broth and Greek yogurt over low heat until the sauce is smooth and slightly thickened.
Steam the broccoli florets until tender-crisp, about 3-4 minutes.
Add the cooked pasta, steamed broccoli, and sliced chicken to the skillet with the sauce.
Toss everything together until well coated, then sprinkle with the Parmesan cheese before serving.