Heat the oven to 425°.

Slice the zucchini and yellow squash into ¼-inch coins and the shallots into thin rings. Strip the thyme leaves from their stems. Mince one of the garlic cloves, leaving the others whole.

Toss the zucchini and squash with ¼ cup olive oil, 1 tsp salt, the minced garlic and half of the thyme, then arrange the vegetables in a ring around the edge of a 12-inch cast iron skillet, leaving the center open.

Stuff the chicken cavity with lemon quarters, whole garlic cloves and a teaspoon of salt. Combine the remaining thyme, the remaining two teaspoons of salt, and two tablespoons of olive oil. Rub this mixture all over the chicken, easing some of the thyme under the skin of the breasts if you can. Truss the legs and set the bird breast-side up in the center of the skillet, tucking the wings underneath.

Roast until the zucchini is tender and the thickest part of the chicken breast reaches 160° on an instant-read thermometer, 60–75 minutes. (It’ll rise to 165° as it rests.)