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1
To roast the garlic: Heat oven to 400 degrees F. Peel away the outer skin of 1 garlic head, and cut off top 1/4 to 1/2 inch of the head to expose the individual cloves. 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, then squeeze the cloves from their skin. Mash 3 cloves and set aside -- reserve the rest for another use.
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2
In a medium bowl, whisk the egg yolks. Gradually whisk in the remaining olive oil, then the grapeseed oil; begin with small drizzles, then whisk in a thin stream until the mayo is very thick. Whisk in a pinch of salt and then the orange juice, a little at a time (you may not need the full amount), orange zest and the roasted garlic paste. Season to taste with salt and pepper.
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3
In a large saute pan, heat 2 tablespoons olive oil over medium heat. Add the fennel and shallots and cook until they start to caramelize, about 8 minutes. Add the red bell pepper and cook about 3 minutes longer; you want the pepper to soften but retain its texture. Remove from the heat. Mix in the fennel fronds, chives, and orange zest.
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4
In a bowl, combine the shrimp with the sauteed vegetable-herb mixture and salt and pepper (to taste). Fold in aioli, a teaspoon at a time, to just bind the burgers. Form into four patties, and refrigerate until ready to cook.
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5
Heat the remaining 3 tablespoons olive oil in a pan (cast iron works well) over medium-high heat and fry the patties until golden, about 4 minutes on each side, or until cooked through.
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6
Spread the aioli on both sides of the toasted buns; serve the shrimp burgers with your favorite condiments, such as a big leaf of butter crunch lettuce.
