In a zip top bag combine chicken breasts, olive oil, lemon juice, and garlic. Allow chicken to marinate for 1 hour.
Preheat an outdoor grill to medium heat. Add chicken breasts to hot grill. Cook chicken for 5-6 minutes per side.
Place an iron skillet on your outdoor grill. Fill the skillet with oil add Brussels sprouts. The sprouts should take about for minutes per side. Sprinkle with salt and pepper. When slightly soft and charred remove skillet from the grill.
In a bowl, whisk together the mayo, yogurt, mustard, and vinegar. Stir in salt, fresh basil, and garlic.
Divide quinoa between 4 bowls. Divide the avocado, arugula, cooked Brussels sprouts, pepitas and apples between each bowl. Dollop each green goddess dressing.