To make the roasted garlic: Preheat oven to 400 degrees F. Peel away the outer skin of 1 garlic head, and cut off top ¼ to ½ inch of the head to expose the individual cloves. Place a piece of foil, large enough to completely wrap the entire head of garlic in, on your counter. Place your garlic in the middle of the foil. Drizzle 1 tablespoon olive oil over the garlic head, wrap in foil, and roast for 30 to 35 minutes, or until cloves are soft when pressed. Cool, and when you comfortable hold the garlic head in your hand, squeeze the cloves from their skin in to a small bowl. Remove 3 cloves to another small bowl, mash and set aside. In the original bowl mash the rest of the garlic and store in your fridge for future use.
In a medium bowl, whisk the egg yolks. Gradually whisk in the remaining olive oil, then the grapeseed oil. Whisk in a very thin stream, very slowly until the mayo is very thick. Whisk in a pinch of salt and then add orange juice, 1/2 tablespoon at a time (you may not use all of the juice), orange zest and the roasted garlic paste. Season to taste with salt and pepper. Taste and see if you want to add another 1/2 tablespoon of orange juice.
In a large sauté pan, heat 2 tablespoons olive oil over medium heat.
Add the fennel and shallots and cook until they start to caramelize and turn light golden brown, about 8 minutes. Add the red bell pepper and cook about 3 minutes. You want the bell pepper to soften but not completely break down. Remove from the heat. Mix in the fennel fronds, chives, and orange zest.
In a bowl, combine the shrimp with the sautéed vegetable-herb mixture and salt and pepper. Fold in 1 tablespoon aioli, a teaspoon at a time, to just bind the burgers. You won't use all the aioli, but just enough for the burgers to hold their shape. Form into four patties, and refrigerate until ready to cook.
Heat the remaining 3 tablespoons olive oil in a cast iron pan over medium-high heat and fry the patties until golden, about 4 minutes on each side, or until cooked through.
Spread the aioli on both sides of the toasted buns. Serve the shrimp burgers with your favorite condiments like coleslaw, pickled red onions or iceburg lettuce leaves.