To make the aioli, whisk together the egg yolk, lemon juice and kosher salt in a metal bowl. Combine the oils together, and begin to slowly whisk into the egg mixture, adding about 1 teaspoon at a time. Keep whisking until thickened and emulsified. Season with black pepper and additional lemon juice, to taste.
In a mixing bowl, combine tuna, shallot, garlic, capers, parsley, mint, aioli (or mayonnaise), lemon juice, 2 tbsp olive oil and salt & pepper. Fold gently, until just combined. Carefully fill each pepper with a heaping tablespoon of the tuna mixture. Once all are filled, set aside.
For the fennel salad, mix together the remaining olive oil, sherry vinegar and salt & pepper in a large bowl. Add in shaved fennel, a handful of torn fennel fronds, arugula, parsley and olives, tossing in the vinaigrette until dressed.
Place three stuffed peppers on each plate, followed by a portion of the fennel salad. Serve with crusty bread, if desired!