Make the dressing. Mix together the apple cider vinegar and non-dairy milk, and let sit for 10 minutes. It will curdle, which is what you want.
Mix the curdled milk, cashews, mustard, garlic, and salt together in a food processor or high-speed blender until smooth and creamy. Add the parsley and chives and pulse a couple times to combine.
Blanch the asparagus. Prepare a large bowl with ice water. Bring a large pot of salted water to a boil. Add the asparagus and cook for 2 to 4 minutes (depending on thickness), until bright green. Remove the asparagus pieces from the pot with tongs or a skimmer, and immediately transfer them to the ice water bowl. Let them sit in the ice water for a minute. Drain and pat dry.
Assemble the salad. Add the lettuce, watercress, radicchio, asparagus and chickpeas to a large bowl. Add about half of the dressing, and toss to coat. Top with the almonds, parsley and feta, and then drizzle on the rest of the dressing.
Divide among 4 plates and serve.