In large wide-mouth jar or bowl, place green pepper slices. In separate bowl, place sugar and salt and add 2/3 cup (160 mL) boiled water; stir until sugar and salt are dissolved. Stir in cider vinegar. Let cool for a few minutes and then add vinegar mixture to peppers. Cover and chill for at least 2 hours or up to several days.
Half-fill medium saucepan with salted water and bring to a boil. Add snap peas and boil for 1 minute. Using slotted spoon, transfer peas to bowl of ice water to halt the cooking process.
Working with 1 asparagus spear at a time, use vegetable peeler to shave spears into long, thin shavings. Thinly slice remaining tips.
To make dressing, in blender container, place olive oil, 2 Tbsp (30 mL) water, lime juice, avocado, basil, parsley, green onions, garlic, and salt, and blend until smooth. Add more water, 1 Tbsp (15 mL) at a time, if needed to help with blending and to reach a desired smooth consistency.
To assemble salad, divide lettuce among serving plates or large bowls. Top with beans, pickled green peppers, cucumber, peas, and asparagus. Add dollops of dressing and scatter with pistachios.