Heat the oil in a large saucepan. Add the onion and carrot, cook for 5 minutes until softened.
Add the bacon bits or diced ham and cook for 2 minutes until starting to colour.
Tip in the split peas, potato and bay leaf. Pour in the vegetable stock and stir well.
Bring to the boil, then reduce the heat and simmer for 45-50 minutes until the split peas are completely soft and the soup is thick.
Remove the bay leaf. Season with salt and pepper. Give it a good stir - the peas will have broken down to make it naturally creamy.
Serve with crusty bread. Add a splash of water when reheating if it has thickened too much.