Holding an asparagus spear in both hands, bend the spear until it breaks naturally at the point where the spear becomes tough. Discard the tough end. Repeat with the remaining asparagus. Cut off the tender tips and reserve.

Bring a large pot of salted water to a boil over high heat. Add the asparagus tips and cook briefly, just until they lose their raw taste. Lift them out with a sieve or skimmer and let cool. Add the remaining portion of the asparagus spears and cook until tender enough to puree, then drain well.

Put the asparagus spears in a blender or food processor with the ascorbic acid, basil, 3 tablespoons of the olive oil, and salt and pepper to taste. Puree until smooth.

In a large bowl, combine the croutons, asparagus tips, peas, and green or spring onion. Add some of the asparagus puree and toss to coat well. Add more puree as needed to coat lightly and evenly. Add 1 1/2 tablespoons of the lemon juice and toss again. Taste and adjust the seasoning, then make an even layer of the mixture on a platter.

In another bowl, combine the radicchio and spinach or arugula. Dress with the remaining 1 tablespoon olive oil, the remaining 1/2 teaspoon lemon juice, and salt and pepper to taste. Toss well, then mound on top of the dressed croutons. With a cheese plane or vegetable peeler, shave some ricotta salata over the top. Serve immediately.