Step 1: In a skillet just large enough to hold them in a single layer, cover teh chicken breasts with cold water.
Step 2: Stir in 2 teaspoons of salt, set the skillet over medium heat, and bring slowly just to a simmer, about 15 minutes, tuning the chicken breasts once.
Step 3: Stir in the shrimp and simmer until they are pink, curled, and just cooked through, about 4 minutes. With a slotted spoon remove the shrimp.
Step 4: Let the chicken breasts cool in the poaching liquid to room temperature. Drain them, remove any fat, and cut out the tough central cartilage from each breast.
Step 5: Line a platter with alternating leaves of radicchio and lettuce. Slice the chicken breasts on the diagonal.
Step 6: Arrange the chicken and shrimp on the leaves and drizzle some of the dressing over them. Garnish with the springs of basil.
Step 7: Serve, passing the remaining dressing separately and offering guests a pepper mill.
Step 8: In a food processor fitted with the metal blade, combine the basil, egg, egg yolk, lemon juice, salt, and pepper.
Step 9: Process for 1 minute or until smooth.
Step 10: With the machine running, pour in the olive oil and corn oils in a steady stream. Adjust the seasoning, if necessary, and serve.
Step 11: (The dressing can be made a day ahead. Refrigerate, allowing it to return to room temperature before using).
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