In a large skillet, melt butter over medium heat. Add onions and sweat them 15 minutes; - do not let brown. Once the onions are sweet and tender, add livers and raise heat just a bit. Cook until livers are firm and cooked through, another 5 to 6 minutes.
While livers cook, place bread on a cookie sheet and bake in oven to dry out and toast, 5 to 6 minutes. Cut toasted bread slices corner to corner. Pile toast triangles into a bread basket.
Combine salt, pepper and thyme and sprinkle over the livers and onions. Place mixture in food processor in batches and grind into smooth spread. Transfer to a serving bowl.
Fill ramekins or other small dishes with cornichons, shallots, mustard, and capers and arrange around the warm spread and toast basket.
Tip: Rachael builds her toast like this: mustard, liver spread, shallots, capers and a pickle on top! YUM-O! Leftover spread can be chilled for several days.