How to Make It
In a bowl, toss all of the ingredients together and season with salt. Let stand at room temperature for 2 hours.
In a food processor, combine the avocados, cilantro, basil and lime juice and puree. Season with salt. Scrape the dip into a bowl and refrigerate until chilled.
In a bowl, toss the shrimp with the fennel, mustard, red pepper and 1 tablespoon of the oil; season with salt.
In a skillet, heat 1 tablespoon of the oil. Add half of the shrimp and cook over moderately high heat, turning once, until just cooked, 3 minutes. Transfer the shrimp to a platter. Wipe out the skillet and repeat with the remaining oil and shrimp. Serve with the salsa and dip.