Heat dutch oven or cast iron skillet on high heat. Once hot, add oil and butter and slightly reduce heat. Sear ribs on all sides, about 8 minutes, turning every 30 seconds. There should be a nice brown crust once you're finished. Remove from skillet and set aside.
Add shallots to the skillet, adding a little more oil and butter if there isn't enough fat. Saute until brown and then add carrots and celery. Sweat for about 20 minutes on low heat.