Put the cornbread cubes, ciabatta cubes, carrots, celery and onion on a baking sheet, drizzle on the oil and toss together with your hands. Nestle the chicken thighs skin-side up among the bread and vegetables. Mix together the salt, pepper, sage and thyme in a small bowl and sprinkle it all over the chicken, bread and vegetables. Dot the top with the butter.
Roast for 15 minutes, then remove and stir the bread and vegetables with a wooden spoon, coating them in the butter. Do not disturb the chicken. Return the baking sheet to the oven and continue roasting until the chicken is completely cooked and the skin is golden and crisp, 25 to 30 minutes. Stir the bread and veggies once more and serve!
Preheat the oven to 450 degrees F.
Stir the cornmeal, flour, baking powder and salt in a bowl to combine. Measure the buttermilk and milk in a measuring cup and add the egg. Stir together with a fork. Add the baking soda and stir. Pour the milk mixture into the dry ingredients. Stir with a fork until combined.
Melt 1/4 cup of the shortening in a small pan on the stovetop or in the microwave in a small bowl. Slowly add the melted shortening to the batter, stirring until just combined.
In a cast-iron skillet, melt the remaining 2 tablespoons shortening over medium heat. Pour the batter into the hot skillet and spread to even out the surface. (The batter should sizzle.) Cook on the stovetop for 1 minute, then bake until the top is golden brown and the edges are crispy, 20 to 25 minutes.