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 final 3 minutes of pasta cooking, add the broccoli florets to the boiling water to blanch them until bright green.
Reserve 0.25 cup of the starchy pasta water before draining the pasta and broccoli.
Season the chicken breast with sea salt and black pepper on both sides.
Heat olive oil in a skillet over medium-high heat and sear the chicken for 5-6 minutes per side until fully cooked, then set aside to rest for 2 minutes before slicing into strips.
In a small mixing bowl, whisk together the Greek yogurt, grated parmesan, minced garlic, and a pinch of nutmeg until smooth.
Return the cooked pasta and broccoli to the pot over low heat, then stir in the yogurt mixture and the reserved pasta water, tossing gently until the sauce becomes creamy and coats the noodles.
Divide the pasta into a bowl, top with the sliced chicken, and serve immediately.