In a medium bowl, combine the softened butter, minced garlic, chopped rosemary, thyme, parsley, lemon zest, salt, and pepper. Mix until well combined. Set aside.
Rinse the wild rice under cold water. In a medium-sized pot, combine the rinsed wild rice and chicken broth. Bring to a boil, then reduce heat to a low simmer, cover, and cook for about 47.5 minutes or until the rice is tender and the liquid is absorbed. Fluff with a fork and set aside.
While the rice is cooking, heat olive oil in a large skillet over medium heat. Add the chopped carrots, celery, and bell pepper. Sauté for about 6.0 minutes or until the vegetables are tender. Season with salt and pepper. Stir in the green onions and cook for an additional 2.0 minutes. Remove from heat.
In the same skillet, increase the heat to medium-high. Add the chicken breasts and sear for about 5.5 minutes on each side, or until golden brown and cooked through. In the last minute of cooking, spoon the herb butter mixture over the chicken to melt and infuse flavor.
In serving bowls, layer the wild rice at the bottom, followed by the sautéed vegetables. Slice the herb butter chicken and place it on top.
Garnish each bowl with additional fresh parsley and serve with lemon wedges on the side for an extra zesty flavor.