Preheat the oven to 425 degrees . Place the chicken in a large cast-iron skillet. Rub with 1 tbsp. oil; season with salt and pepper. Stuff 5 sprigs thyme in the cavity. Using kitchen twine, tie the legs together. Roast 25 minutes.
In a large bowl, toss the cauliflower, tomatoes, shallots, and the remaining 5 sprigs thyme and 2 tbsp. oil; season.
Arrange the vegetable mixture around the chicken. Roast, stirring the vegetables after 20 minutes, until the cauliflower is browned and tender and an instant-read thermometer inserted into the thickest part of the chicken thigh registers 165 degrees , about 35 minutes more. Transfer the chicken to a platter.
Add the wine to the skillet and stir until reduced slightly, about 1 minute. Sprinkle the vegetables with the chopped thyme; serve with the chicken.