Heat the oil in a flameproof casserole dish and stir-fry the red onion for 5 minutes until it starts to soften. Stir in the thyme and garlic, season well, and cook for 1 minute.
Add the sausages to the pan and brown them on each side. Take the onion and sausages out of the pan and set them aside. Add the butter and plain flour and stir for about a minute to make a paste. Slowly add the stock, stirring constantly to make a smooth sauce. Stir in the tomato purée and Worcestershire sauce.
Put the onions and sausages back in the pan and put the lid on. Bring to a gentle simmer, then cook for 20–25 minutes, stirring every now and then.
To make the mash, put the root veg in a saucepan, cover them with cold water and add salt. Put a lid on the pan and bring to the boil. Simmer for about 20–25 minutes until all the vegetables are very tender. Drain them, then tip them back into the pan. Put the pan back on the turned-off hob and leave for a minute or so to steam-dry the veg. Add the milk and butter, then season and mash until smooth.
Serve the mash with the sausages and spoon the gravy over the top. Garnish with parsley and serve with green veg.