For the batter, whisk together the milk, flour, eggs and 120ml/4½fl oz water in a bowl. Cover and refrigerate for at least 20 minutes.
Preheat the oven to 220C/425F/Gas 7.
Heat the beef dripping in a large pan over a moderate heat.
Sit the shallots in the pan cut-side down, and cook until softened.
Add the carrots and garlic and cook until they have browned and caramelised - about five minutes.
Transfer the pan ingredients to an oven dish, add the thyme, season with salt and freshly ground black pepper and place in the oven to get piping hot for five minutes.
Once the dripping is sizzling hot, open the oven door and tip the batter over the vegetables as quickly as possible, so not to lose too much heat.
Bake for 20-30 minutes, or until the pudding is well risen and golden-brown .
Serve quickly as otherwise the pudding will deflate.