Preheat the slow cooker if necessary; see the manufacturer's instructions. Heat the butter and oil in a saucepan, add the onion and fry, stirring, for 5 minutes or until softened and just beginning to brown.
Stir in the garlic and rice and cook for 1 minute. Add all but 150 ml (¼ pint) of the stock, season with salt and pepper, then bring to the boil. Transfer to the slow cooker pot, cover with the lid and cook on low for 1¾–2 hours.
Stir in the pesto and the remaining stock if more liquid is needed. Place the frozen vegetables on top of the rice, replace the lid and cook for another 20–30 minutes or until the vegetables are hot. Serve, garnished with Parmesan shavings and basil leaves.