HEAT A 6-QUART DUTCH OVEN with the oil and butter over medium-high heat for two minutes. Sprinkle the drumsticks with kosher salt and fresh ground pepper, along with the pinch of crushed red pepper. * Add the seasoned chicken to the hot pan and cook for about 5 minutes or until well-browned on one side. Turn and brown the other side. Remove chicken to a plate and cover.
SAUTÉ THE ONION, celery, and carrot, Herbes de Provence, and another 1/2 teaspoon salt and ¼ teaspoon pepper in the Dutch oven for about 10 minutes – or until softening, stirring often. Add minced garlic and stir. Cook another minute before pouring in the white wine. Simmer until the wine is nearly all absorbed.
STIR IN THE RICE, cook for one minute, and pour in both the can of tomatoes and chicken stock. Return the browned drumsticks to the pan and push them down into the rice mixture just a bit. Reduce heat to a simmer, cover, and cook for 10 minutes or so.
SPRINKLE IN THE BELL PEPPER AND ZUCCHINI on top of the chicken and rice and simmer another 10-15 minutes covered or until rice and vegetables are tender and an instant read thermometer placed in the drumsticks registers at 170 degrees F or above. Check a time or two to make sure rice isn’t dry before it’s done and add a little extra broth or water if needed. Taste and adjust seasonings.
SERVE HOT, fluffing rice as you spoon it into shallow serving bowls and garnish with cheese and basil, if using.
Store leftovers well-wrapped in the refrigerator for no more than 3 days. Reheat leftovers covered over low heat, adding a little water to maintain moistness and adjusting seasonings once more. Do not freeze.