Bring a pot of salted water to a rolling boil. Remove the woody stock from the asparagus and discard. Cut the asparagus in half and add to the boiling water. Cook for 3-4 minutes and remove from the water, strain, and cool completely. Blanch the green beans for 3-4 minutes and remove from the water. Allow to drain and cool.
Measure the frozen peas and remove the frost by running them under water. Set aside until assembling.
Drain and roughly chop the artichokes.
Peel the avocado and dice.
Chiffonade the basil leaves. To chiffonade, lay all the basil leaves on top of each other and roll into a tight bundle. Cut the bundle into thin strips.
To make the dressing, whisk together olive oil, lime juice, honey, and water. Season with salt and pepper, and add the basil leaves.
Assemble the salad by adding all the vegetables to the arugula and toss with the dressing.