Heat the vegetable oil in a large casserole pot over a medium/high heat. Brown the sausages all over, in batches if necessary, and set aside.
Lower the heat slightly and add the baby onions. Brown these all over then add the chopped swede and carrots. Cook for 5 minutes then add the garlic and cook for a further 1 minute.
Return the sausages to the pan. Add the stock, bay leaf and thyme and season with freshly ground black pepper. Add more stock if necessary to just cover the vegetables. Bring to a simmer and cook gently with the lid on for the first 20 minutes. Remove the lid and continue to simmer for a further 20 minutes or until the vegetables are tender and the sauce has thickened.
Once the stew has finished cooking, stir through the pesto and serve with the bread if using.