Heat a large frying pan with a lid to medium-high heat. Once hot, add 3 tablespoons of schmaltz. Once it has heated, add the onions and toss them in the fat to evenly coat, cooking them for one minute.

Cover the pan and reduce the heat to medium-low and let them slowly steep for 15 minutes, checking in every 5 minutes to give them a stir.

Uncover the pan, raise the heat to medium and stir in salt. Cook onions, stirring occasionally, for another 15 minutes.

Increase heat to medium-high and cook onions until browned at the edges and utterly delicious. Add madeira and vinegar and scrape up any onion bits stuck to the pan. Cook, stirring, until both liquids disappear and the onions are dark. Transfer onions to a large bowl.

Add 3 more tablespoons schmaltz to the empty pan and heat over medium-high. Add the livers in one layer and season very well with salt and pepper. Cook for 3 minutes, until lightly browned underneath and flip the livers, seasoning again with salt and pepper, and browning them on the second side, about 2 minutes.

Add the livers to the bowl with the onions, pour the last 1 to 2 tablespoons of schmaltz over, and let everything cool completely.

In a food processor, blend the liver and onions until absolutely smooth and as whipped as you can get it. Taste for seasoning; adjust salt and pepper as needed.

Transfer to a serving bowl. If you’ve reserved cooked onions, scatter them on top. Serve with crackers and garnishes of your choice.