Preheat oven to 375°F. Rub the chicken with oil, garlic powder, lemon zest, thyme, salt and pepper.
Set the chicken in an oven-safe skillet or sauté pan, skin side up. Roast for 35-45 minutes, until a thermometer inserted into the thickest part of the meat, (not near a bone), registers 160°F. Transfer the chicken to a carving board and let rest for 5 minutes.
In a bowl, whisk the flour with about an equal amount of water, or more if needed, to form a smooth paste.
Place the pan you roasted the chicken in, on the stovetop over medium-high heat. Add in the broth and bring to a simmer. Add in the flour/water mixture a little bit at a time while simmering until the liquid reduces and thickens to a creamy, smooth consistency (use more or less flour/water to thicken to a smooth consistency).
Gently pull out the breast bones from the chicken and portion accordingly. Spoon the pan gravy and serve with dinner rolls. Garnish with a sprig of thyme.