Bring a pot of salted water to a boil and cook the brown rice pasta according to package directions, reserving 2 tablespoons of pasta water before draining.
Season the chicken breast evenly with sea salt, black pepper, and dried oregano.
Heat the olive oil in a skillet over medium-high heat and sear the chicken for 5-6 minutes per side until golden and cooked through, then set aside to rest.
In the same skillet, reduce heat to low and sauté the minced garlic for 30 seconds until fragrant.
Whisk together the Greek yogurt, grated parmesan cheese, and the reserved pasta water in a small bowl until smooth.
Add the cooked pasta to the skillet with the garlic, pour in the yogurt mixture, and toss gently on low heat until the sauce coats the noodles.
Slice the rested chicken and serve it over the pasta, garnished with fresh chopped parsley.