How to Make It
In a pot, cover the bacon, pig's foot and whole onion with the water and boil. Simmer over moderately low heat until the foot is tender, 3 1/2 hours. Strain the broth and return to the pot, reserving the bacon and pig's foot.
Boil the broth until reduced to 2 quarts, 25 minutes; skim off the fat or refrigerate overnight and then skim off the fat. Remove all the lean meat from the bacon and pig's foot, cut into bite-size pieces and reserve.
Meanwhile, in a large pot, heat the rendered fat. Add the sliced onions and season with salt. Cover and cook over high heat, stirring, until the onions are wilted, 15 minutes. Reduce the heat to moderate and cook until the onions are very soft, 30 minutes. Uncover and cook over moderately high heat, stirring, until the onions are lightly browned, 10 minutes. Remove from the heat and stir in the flour until smooth.
Return the pot to the burner. Add the strained broth, ale and 4 of the rosemary sprigs and cook over moderately low heat, stirring, until the soup thickens. Simmer the soup for about 15 minutes, until no floury taste remains. Add the reserved meat and season the soup with salt and pepper. Discard the rosemary.
Preheat the oven to 350°. On a rimmed baking sheet, toss the bread cubes, melted butter, garlic and the remaining 2 rosemary sprigs; season with salt and pepper. Bake for 30 minutes, until the croutons are crisp. Discard the rosemary and garlic.
Preheat the broiler. Ladle the soup into heatproof bowls on a baking sheet and top with the croutons and cheese. Broil for about 2 minutes, until bubbling, and serve.