In a large, heavy-bottomed pot, melt the butter and the lard over low heat.
Add the onions and cook slowly, allowing them to develop a rich brown color. Once the onions have cooked for about 20 minutes, add the flour and stir through.
Add the wine, milk and stock, then gently stir. Cook 10 minutes more, at a high simmer.
Whisk in the eggs and cheese and continue to cook until the liquid thickens to stew consistency. Season with salt and pepper. Grill each slice of bread, drizzle with oil and serve with the cipollata in warmed bowls.
In a large, heavy-bottomed saucepan, heat the oil over high heat until smoking.
Add all the chicken parts and brown all over, stirring to avoid burning.
Remove the chicken and reserve.
Add the carrots, onions, and celery to the pot and cook until soft and browned. Return the chicken to the pot and add 3 quarts of water, the tomato paste, peppercorns, and parsley. Stir with a wooden spoon to dislodge the browned chicken and vegetables bits from the bottom of the pan. Bring almost to a boil, then reduce heat and cook at a low simmer until reduced by half, about 2 hours, occasionally skimming excess fat.
Remove from heat, strain, and press on the solids with the bottom of a ladle to extract out all liquids. Stir the stock to facilitate cooling and set aside. Refrigerate stock in small containers for up to a week or freeze for up to a month.
