Then add the pasta and toss until it’s cloaked in the sauce. It should come together as well as a classic pesto—even better. “I think I now prefer this to the original,” Mr. Bottura said.

3. While the pasta is cooking, cut the asparagus into 1 inch pieces. Add the pieces from the bottom third of the stalks to a small food processor. Pulse the asparagus along with the radish leaves ...