Make the fava: Heat a tablespoon of olive oil and cook the chopped onion until very soft and lightly colored. Add the fava and stir to coat in the oil. Add enough water to cover the fava by about an inch and simmer, replenishing the water, until the fava is soft and thick as mashed potatoes and has absorbed all the liquid, about an hour. Season with salt. Remove and puree with an immersion blender, adding additional olive oil and a touch of red wine vinegar. Set aside covered and let cool completely.

Combine the cooked fava with the parsley and mint. Adjust salt level to taste. Add the egg yolk and enough breadcrumbs to form a dense mixture that holds its shape when formed into a 3- or 4-inch burger. Shape the burgers. Chill for one hour to firm up.

While the fava burgers are chilling, prepare the onion topping: in a non-stick pan over medium heat, add 1 tablespoon olive oil and cook the onions for about 25 minutes, until deep amber and nicely caramelized. Set aside.

Drizzle about a teaspoon or two of olive oil in a hot non-stick or cast iron pan and cook the fava burgers a couple at a time, flipping once, carefully, until browned and golden.

Toast the bread buns. Spread one or both sides with the tomato paste. Place a burger on the bottom half of each bun. Top with arugula and caramelized onions and spoon a few capers over the top. Serve.