1 3½–4-pound whole chicken
2 fennel bulbs, cut into 6 wedges each
1 pound small carrots, scrubbed, cut into 4-inch-long pieces on a diagonal
3 tablespoons olive oil, divided
Pat chicken dry with paper towels and season generously with salt, inside and out. (We use 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt per lb.) Tie legs together with kitchen twine. Let sit 1 hour to allow salt to penetrate, or chill, uncovered, up to 1 day ahead.
Place a rack in upper third of oven and set a 12″ cast-iron skillet or 3-qt. enameled cast-iron baking dish on rack. Preheat oven to 425°.
Meanwhile, toss fennel, carrots, and 2 Tbsp. oil in a large bowl to coat; season with salt and pepper.
Once oven reaches temperature, pat chicken dry with paper towels and lightly coat with half of remaining oil. Drizzle remaining oil into hot skillet (this helps keep the chicken from sticking and tearing the skin). Place chicken in the center of skillet and arrange vegetables around. Roast until fennel and carrots are golden brown in spots and tender an instant-read thermometer inserted into the thickest part of breasts registers 155°, 50–60 minutes (temperature will climb to 165° as chicken rests). Let chicken rest in skillet at least 20 minutes and up to 45 minutes.
Transfer chicken to a cutting board and carve. Serve with vegetables.