To make the aioli: Warm the olive oil over low heat in a large skillet. Add the garlic, paprika, and cayenne pepper and toast until the garlic is fragrant, about 3 minutes. Remove the pan from the heat and add the vegetable oil then transfer the mixture to a measuring cup.
Combine the egg yolks, lemon juice, red wine vinegar, Dijon mustard, salt, and pepper in a food processor, blender or mixing bowl. Gradually incorporate the garlic mixture, processing, blending, or whisking continuously as you emulsify. Chill the aioli thoroughly.
To poach the shrimp: Combine 1 1/2 quarts of water with 5 bay leaves, the lemon juice, wine, cayenne pepper and salt in a large saucepan. Bring the poaching liquid to a simmer over medium-high heat. Add the shrimp and cook until they are pink, firm and opaque, about 5 minutes. Drain the shrimp and allow them to cool.
Put the shrimp in a bowl. Add aioli and mix well. Spoon the shrimp onto plates and serve.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.