Pre-heat the oven to 200°C/400°F/gas 6.
Cut the carrots, celery and onions into 5 mm (¼ in) dice. Sweat with the garlic in the olive oil and butter for a few minutes in a flameproof casserole dish. Add the split peas and cook for 1–2 minutes, stirring. Cover with the stock and bring to the simmer. Cover and cook in the pre-heated oven for 20–25 minutes. The peas will need stirring during cooking, and possibly more stock will need to be added. After 30 minutes the peas should be ready, just starting to break and tender to eat. Season with salt and pepper before serving.