Combine the rice, shallot, chile, garlic, 2 tablespoons of the cilantro, the almonds, lime zest, salt, pepper, 2 tablespoons of the breadcrumbs and the egg yolks together in a medium bowl. Mix with your hands combining all ingredients well until it all sticks together. Take 1 tablespoon of the stuffing and squeeze it gently in your hand to compress it into a tight sausage-like shape. Place the stuffing inside of a sardine and flatten it so that it sticks to the sardine. Repeat with the remaining stuffing and sardines.
Mix the remaining breadcrumbs and cilantro together on a large plate. Add the egg whites to a medium bowl and use a whisk to whip the whites until they are frothy, about 1 minute. Dip a sardine into the frothy whites, then place it in the breadcrumbs, coating both sides with the breadcrumb mixture. Set on a plate and then repeat with the remaining sardines.
Heat 1/4 cup of the olive oil in a medium skillet over medium heat. Add 2 sardines to the pan stuffing-side down and fry, using a spatula to press down on the sardines gently, until browned, about 2 minutes. Turn the sardines over and brown the other side for about 2 minutes more. Transfer to a paper towel-lined plate and repeat with the remaining sardines.
Add the arugula to a medium bowl and drizzle with the remaining 1/4 cup of olive oil. Season with salt and pepper and toss to combine. Divide the arugula among 6 plates and add a fried sardine to each. Serve with a lime wedge.
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