It is recommended to salt the chicken overnight. Pat the chicken dry and remove any strings. Liberally sprinkle kosher salt all over the surface of the chicken, even on the back. Place the chicken on a plate and cover. Refrigerate overnight.
Remove the chicken from the fridge two hours before you intend to roast it. Remove any covering and pat the chicken dry. Allow to come up to room temperature uncovered to allow the skin to dry off.
While the chicken is air drying you can prepare the compound butter. Using a mortar and pestle, grind the dried chamomile flowers until crumbled. In a small bowl add the chamomile, fresh thyme, zest of 1 lemon, 1 tsp kosher salt, and 1/4 tsp pepper to the softened butter. Mix well. Remove 2 tablespoons of the butter and set aside for later.
Cut the lemon in half, reserving one half to stuff the chicken while slicing the remaining half. Cut a thick slice from the onion and set aside to stuff the chicken; cut the remaining onion into slices. Drizzle a large roasting pan with 2 tablespoons olive oil. Scatter in the sliced onion, lemon slices, garlic cloves, and 4-5 sprigs of fresh thyme. Place a rack on top of the aromatics.
Preheat the oven to 400°F. Transfer the chicken to the roasting pan. Stuff the cavity with the remaining pieces of onion and lemon along with 2-3 thyme sprigs. Use your fingers to separate the skin from the breast. Rub some of the butter under the skin over each breast. Use twine to tie the legs together and then tuck the wing tips under the chicken. Rub the remaining butter evenly over the whole chicken.
Roast the chicken for 1 hour 15 minutes to 1 hour 45 minutes depending on the size. Baste the chicken regularly with the pan drippings as it roasts. The chicken is done when it reaches an internal temperature of 165°F. Another way to tell the chicken is done is to tip the pan and check that the juices running from the cavity are no longer pink. Remove the chicken to a platter and let rest before carving.
While the chicken is roasting, peel the carrots, cutting them in half if they are large. Trim the asparagus. Bring a deep skillet of water to a boil, salting the water generously. Prepare an ice water bath in a large bowl.
Add the carrots to the boiling water and let simmer for 4 to 6 minutes until they begin to soften. Add the asparagus and cook for another 2 to 3 minutes until they begin to soften. Transfer the cooked vegetables to the ice water bath to stop them cooking. Pat the vegetables dry and set aside.
Transfer the chicken to a cutting board and set aside. Remove the rack and any large pieces of vegetables or herbs from the pan. Leave 1/3 cup of the drippings in the roasting pan. Place the roasting pan over medium high heat.
Add the flour to the roasting pan and whisk into the fat to make a roux. Let the roux cook for a minute and then deglaze with the dry vermouth. Add the chicken broth, half a cup at a time, whisking constantly to prevent lumps. Bring the gravy to a boil and cook until thickened. Add more broth if desired to thin out the gravy. Season with kosher salt and pepper to taste. Strain the gravy through a fine mesh strainer.
Before serving finish the vegetables. Place a large skillet over medium high heat. Add 1 tablespoon olive oil to the skillet along with the snap peas. Sauté for 2 to 3 minutes until they begin to brown and then add the thawed frozen peas. Season with kosher salt and pepper. Cook for another couple of minutes and then stir in half of the remaining compound butter.
Add the carrots and asparagus to the pan, tossing with the peas. Add the remaining compound butter and continue cooking until all the vegetables are heated through.
To serve, carve the chicken into pieces. Cut the legs off each side of the chicken and then split the drumstick from the thigh. Cut the wings off. Slice each breast off the breastbone. Slice each breast into 3 or 4 slices. Arrange the chicken on a serving platter with the spring vegetables. Serve with the pan gravy and enjoy!