Preheat oven to 400°F.
Place a large skillet in the preheated oven for 10 minutes.
Place thigh pieces, skin-side down, onto your work surface.
Cut one of the thick ends of the carrots the same length as the width of the thigh; this carrot will replace the bone.
Reconstruct the thigh around the carrot and tie well, as shown.
Cut the rest of those two carrots into 2-inch pieces and add to the others.
Lightly rub the skin with olive oil.
Mix the chopped herbs and rub onto both sides of the turkey thighs; season with salt and pepper. When the skillet is well heated, place thighs skin side down in the skillet; they will sizzle. Roast for 20 minutes.
Add the potatoes, shallots, carrot pieces, bay leaves, and the rosemary branches sprigs.
Sprinkle all with a little more salt and pepper, then drizzle some olive oil on top. Roast for another 30-40 minutes, stirring the potatoes and shallots once during roasting, until thighs are done and potatoes are tender.
Remove pan from oven, cover with foil, and let rest 10 minutes.
Place turkey – in slices – and vegetables on a serving platter.
Use pan drippings to make gravy with flour and chicken stock (about 2 cups), if desired.