In a small bowl, combine the lemon juice and shallot; set aside to marinate for at least 10 minutes.

In a blender or food processor, combine the rockfish, egg yolks, and mustard. Pulse the mixture while very slowly pouring in the olive oil until the mixture is thick, smooth, and mayonnaise-like. If the mixture is too thick, add in some of the reserved rockfish liquid as needed to achieve your desired consistency.

Transfer the mixture to the bowl with the marinated shallot, then add the chopped parsley, a few cracks of black pepper, and salt to taste. Stir to combine.

In a medium bowl, toss the green beans with the vegetable oil and a few pinches of salt. Heat a cast iron pan over high heat until smoking, then reduce the heat to medium. Add the green beans and cook, stirring occasionally, until tender and charred, 6-7 minutes. If the green beans are charring on the outside but aren't quite tender, add more of the reserved rockfish liquid and allow the beans to steam for 1-2 minutes.

Place the green beans on a plate or bowl and drizzle them with as much of the “tonnato” as you like. Sprinkle everything with toasted sesame seeds, chili flakes, and bonito flakes, and serve with lemon wedges on the side.