In a 12-inch cast iron skillet, heat 3 tablespoons olive oil over medium heat until almost smoking.
Add the onion, capers, and anchovy paste, and cook until the mixture is golden brown, about 8 to 10 minutes
Add ¼ cup vermouth and balsamic vinegar.
Let reduce.
Add the chicken livers and stir until lightly browned, about 4 to 5 minutes.
Add the remaining ½ cup vermouth. Bring the mixture to a boil. Lower the heat and let the mixture simmer for 15-20 minutes.During this time break the livers up with a wooden spoon as they cook. You are looking for a very rustic, varied texture.Season, to taste, with salt and pepper.
Remove from the heat.Stir in the chili flakes and parsley.Toast the bread until golden brown and place on serving plates.
Spread equal amounts of the liver mixture over 1 side of each piece of bread and serve immediately.