Yields: 4-6 servings
1. Place rack in middle of oven; preheat to 300°. Pat chicken dry with paper towels. Place on a small rimmed baking sheet. Season whole chicken all over with kosher salt and lots of freshly ground black pepper, making sure to season the inside cavity.
2. Whisk miso and ¼ cup sesame oil in a medium bowl until combined. Finely grate 3 garlic cloves (from one of the heads of garlic) and shallot into miso oil. Whisk to combine.
3. Cut what’s left of the head of garlic in half crosswise. Repeat with second head of garlic. Stuff 2 garlic halves inside cavity of chicken. Tie legs together with kitchen twine.
4. Brush half of miso oil over chicken.
5. Toss squash and remaining 2 garlic halves and 2 tbsp. Sesame oil in remaining miso oil until well coated and season lightly with salt and pepper.
6. Arrange squash in a 12" cast-iron skillet, scooting them toward edges of pan to make space for chicken. Nestle garlic halves (cut sides down) in center of skillet. Place chicken over garlic. If any squash pieces have shimmied their way under the chicken, use tongs to arrange them around it.
7. Roast chicken and squash until squash is very tender when pressed with the back of a spoon, and chicken skin is deep reddish-golden brown in color, 2½–3 hours. Transfer chicken to a cutting board and let rest 10–15 minutes.
8. Finish the squash: thinly slice 5 scallions on a long diagonal. Cut orange into quarters. Stir 2 tsp. Maple syrup and juice of one orange-quarter into squash. Taste squash and season with more salt if needed. Scatter sliced scallions over squash.
9. Carve chicken, then arrange pieces over squash and scallions. Serve right out of skillet with remaining orange wedges alongside for squeezing, and squeeze out the sweet, slow-roasted garlic cloves as you wish.