Bring a pot of salted water to a boil and cook the whole wheat pasta according to package directions, adding the broccoli florets during the last 3 minutes of cooking.
Reserve 2 tablespoons of pasta water, then drain the pasta and broccoli.
While pasta cooks, season the chicken breast with sea salt, black pepper, and dried oregano.
Heat olive oil in a large skillet over medium heat and sear the chicken until golden brown and cooked through, about 5-6 minutes per side.
Remove chicken from the pan, let it rest for 2 minutes, then slice into thin strips.
In the same skillet, reduce heat to low and add the minced garlic, sautéing for 30 seconds until fragrant.
Whisk in the Greek yogurt, parmesan cheese, and reserved pasta water until a smooth, creamy sauce forms.
Toss the cooked pasta, broccoli, and sliced chicken into the sauce until well coated and serve immediately.