1. To make the vinaigrette, pulse the garlic in a food processor until chopped. Add the basil and pulse until finely chopped. Add the oil, vinegar, and lemon juice and process until smooth, about 10 seconds. Season with salt and pepper to taste.
2. Place the shrimp in a large resealable plastic bag, add 1/4 cup of vinaigrette and press out any excess air. Seal the bag, then shake to coat the shrimp with the dressing. Marinate the shrimp in the fridge for 30 minutes or up to 24 hours.
3. Preheat a grill or a grill pan on the stovetop to medium-low heat. Lightly oil the grill grates or grill pan with avocado oil. Cook the shrimp until it turns pink on the bottom, about 2 minutes. Flip and cook for 2-3 minutes more, until shrimp is opaque and cooked through. Transfer the shrimp to a plate and let it cool for 10 minutes.
4. Place the baby greens in a large bowl. Add the avocados, nectarines, strawberries, and tomato and toss gently to combine. Sprinkle the cashews and chives over the top, then add the shrimp. Drizzle the salad with 1/2 cup of the dressing. Serve immediately, with the additional dressing on the side.
5. Store any unused dressing in an airtight container in the refrigerator for 1 week. Shake before using.