Preheat oven to 375 degrees F for a standard oven and 350F for convection with convection going.
Mix all of the herbs with the butter, salt, pepper and garlic.
Wash and dry the chicken.
Place your hand gently under the skin over the breast and loosen skin from breast and drumsticks.
Take half of the herbed butter and gently rub it over the breast and drumsticks.
Tie drumsticks together using kitchen twine.
Rub remaining butter over the top of the chicken breast, drumsticks and thighs.
It will clump a bit and that is OK. As it melts in the oven it will cover the bird.
Place the bird in at least a 9 x 13 baking dish or roasting pan.
Place potatoes and carrots around the chicken add 1/4 cup of water and baste every 20 minutes for about an hour and a half until chicken thigh registers 160 degrees F on an instant read thermometer.
Add more water or wine as necessary to have enough juice to baste the chicken with in 1/4 cup increments.
When your chicken hits 160F, add broccoli and baste with pan juice well and bake another 15 minutes until broccoli is tender and chicken thigh registers 165 degrees.