How to Make It
In a medium bowl, whisk the milk with the egg yolks and 1/4 cup of cheese.
Fill another medium bowl with ice water. In a large pot of salted boiling water, blanch the asparagus until bright green and crisp-tender, about 1 minute. Using a slotted spoon, transfer the asparagus to the ice bath to cool. Drain well. Add the pasta to the boiling water and cook just until al dente; drain.
Meanwhile, in a large skillet, heat the olive oil. Add the bell pepper, onion, garlic and crushed red pepper and cook over moderate heat, stirring frequently, until softened, about 6 minutes. Add the chicken, season with salt and black pepper and cook, stirring, until browned, about 3 minutes. Add the asparagus, pasta and milk mixture and bring to a simmer over moderately high heat. Simmer until the chicken is cooked through and the sauce is thickened, about 3 minutes. Stir in the spinach and basil, season with salt and black pepper and cook until wilted, about 1 minute. Divide the pasta among 4 bowls and top with lemon zest and freshly ground pepper. Pass extra cheese at the table.