Heat olive oil in a large skillet over medium heat. Add the chopped white onions and cook, stirring occasionally, until deeply golden, 15 to 20 minutes. Transfer the onions to a bowl.

Add the chicken livers to the skillet, season with salt, pepper, and honey, and cook until browned and just cooked through, about 6 minutes. Transfer to a cutting board and chop finely with a knife, or pulse briefly in a food processor.

Return the chopped liver to the bowl with the onions and mix until evenly combined. Taste and adjust seasoning if needed.

To make the onion jam, heat olive oil in a medium saucepan over medium heat. Add the sliced red onions and cook, stirring, for 3 minutes until they begin to soften.

Stir in the salt, pepper, brown sugar, balsamic vinegar, honey, and water. Reduce heat to medium-low and simmer, stirring occasionally, until the liquid reduces and the mixture becomes thick and jam-like, about 1 hour. Let cool.

Lightly moisten the matzo sheets with water and cover with a towel. Let rest 5 to 7 minutes until flexible. Cut into 3-inch/7.5 cm circles and press into a lightly oiled muffin tin to form cups. Brush with olive oil and bake in a 350°F/180°C oven until crisp and lightly golden, about 8 minutes. Cool completely.

Fill each matzo cup with chopped liver and spoon onion jam over the top. Garnish with fresh dill if desired and serve immediately. For the best texture, fill the cups just before serving so the matzo stays crisp.