Olive Oil-Roasted Chicken With Caramelized Carrots

whole chicken legs, or bone-in, skin-on drumsticks or thighs

Kosher salt and freshly ground black pepper

bunch small, thin carrots, preferably with their green tops

heads garlic, left unpeeled and halved crosswise to expose the cloves

lemon, thinly sliced, seeds removed

bunch oregano, plus more leaves for garnish

olive oil