In a food processor, pulse all the aioli ingredients together to combine, except for the olive oil.

Turn the food processor on and slowly pour in the olive oil for about a minute, or until the aioli forms; turn off the food processor, scrape the sides, and process again until combined.

Place the aioli in the refrigerator until ready to use.

In a large strainer over the sink, add the 5 cans of tuna and let them drain while preparing the remaining ingredients.

Sauté the onions for about 8 minutes in a skillet until translucent and set aside to cool. While the onions cook, add the mayo, lemon juice, salt and pepper in a mixing bowl and whisk until combined; add in the cilantro and jalapeno.

Beat the eggs and add to the mixing bowl along with the tuna, cooked onions, and the cream of chicken packet; mix gently until all ingredients just hold together.

In a large skillet, heat the olive oil on high for about 1 minute then reduce the heat to medium high heat.

Working in batches, pack a 1/3 cup measuring cup with the tuna mixture and place in the skillet without overlapping; cook until the cakes are golden brown and crisp on the outside, about 3 minutes per side. If needed, add 1 tablespoon of oil to the pan between batches.

Serve with the basil aioli.