Heat the oven to 450 F.
Wash the chicken and pat it dry with a paper towel.
Line a baking pan with foil.
Add the cubed potatoes, five whole garlic cloves and carrots, spreading out in an even layer. Season with salt.
In a small bowl, combine the butter, herbes de provence, lemon zest and the remaining garlic clove, minced.
Rub this mixture over the whole chicken, including under the skin.
Place the chicken on top of the bed of vegetables, and season the outside with salt.
Place the halved lemon inside the chicken cavity, and arrange the fresh herb sprigs around the chicken and vegetables.
Roast for 90 minutes, tossing the vegetables every so often in the rendered fat.
Once 70 minutes have gone by, add the asparagus, toss it in the rendered fat and return the pan to the oven to roast for the remaining 20 minutes.
Serve immediately.
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