Step 1Blanch the garlic: Bring a small pan of water to a boil. Carefully drop the cloves in the water and blanch for 30 seconds. Remove the cloves and place in ice water to stop the cooking process and cool the garlic, 1 to 2 minutes. Return the garlic to the boiling water for an additional 30 seconds. Remove and cool again in the ice water. Set aside.
Step 2Shuck the ear of corn and remove the silk. Brush lightly with olive oil and season with a pinch each salt and black pepper. Cook the whole cob over a grill or an open flame on the stove until the kernels are slightly charred. With a sharp knife, remove the kernels from the cob and cool.
Step 3Roast the pepper: Place the pepper over a hot burner until charred on all sides. Remove to a sealed paper bag to rest until cool enough to peel. Peel the charred skin (do not rinse, as this will remove flavor). Halve the pepper lengthwise, then stem and seed. Place the pepper in the bowl of a food processor.
Step 4To the bowl of the food processor, add the mayonnaise, aji amarillo purée, yuzu sauce and garlic, pulsing together to form the aioli. Remove the aioli, cover and refrigerate until needed. This makes a generous 1½ cups aioli, much more than is needed for the remainder of the recipe; the aioli will keep up to 1 week, refrigerated.
Step 5Fill a medium, heavy soup pot with enough oil for deep-frying (the oil should come about 3 inches up the sides of the pan). Heat the oil until a thermometer inserted reads 375 degrees.
Step 6While the oil is heating, place the tempura flour in a bowl. Dredge the shrimp in the flour, shaking off any extra back into the bowl. Whisk together the remaining flour, the egg white and the water to form a batter. When the oil is at the right temperature, dip the shrimp in the batter and carefully fry in the oil until the pieces are golden brown. Drain the shrimp on paper towels.
Step 7In a large bowl, carefully toss the tempura shrimp and corn with enough aioli to coat. Divide the shrimp among 6 bowls and garnish each bowl with 1 shrimp head and the cilantro.