In a large bowl, whisk together the flour, salt, and pepper. Make a well in the center of the flour. Pour in the eggs, milk, and 2 tablespoons melted butter and whisk until the flour is smooth. Cover and let stand 30 minutes.
VERY IMPORTANT TO DO THIS STEP AND PREHEAT THE CASSEROLE DISH. (The batter will not rise correctly) Coat the bottom and sides of an 8"x12" casserole dish with a high smoke point vegetable oil. Set the oven rack in the lower-third of the oven. Place the empty casserole dish on the rack and preheat the oven to 425F
While the oven is heating, heat a tablespoon of oil on a skillet on medium heat. Add the sausages and brown them on at least a couple sides. When the sausages have browned and the dish in the oven is hot, pull the oven rack out a bit. Put the sausages in the casserole dish, and pour the batter over the sausages, throwing the sprigs of rosemary in with the batter. Cook for 20-30 minutes, or until the batter is risen and golden. DO NOT OPEN THE OVEN TOO SOON, OR THE BATTER WILL COLLAPSE.
While the dish cooks, cook the onions and remaining 2 tablespoons butter in the skillet until the onions have softened and browned (about 5 minutes). Add the garlic and thyme and saute 30 seconds or until fragrant. Add the balsamic vinegar and cook it down to about half. Add the bullion cube and stir. Sprinkle with a little water, let simmer, then serve with the toad in the hole.