
Sauté leek and garlic. Heat the olive oil in a large saucepan over medium heat. Add the leek and a generous pinch of salt. Cook until softened, stirring occasionally, about 5 minutes. Add the garlic and cook just until fragrant, about 2 minutes.
Add the orzo. Pour in the orzo and cook, stirring with a wooden spoon, until the pasta is translucent around the edges, about 2 minutes. Add the chicken stock or vegetable broth and bring to a boil over high heat. Partially cover the pan and simmer over medium-low heat, stirring occasionally to prevent sticking, for another 2 minutes.
Add the asparagus. Add the asparagus and return the mixture to a simmer. Cook, covered, until bright green, 2 minutes.
Stir in spinach and peas. Add the spinach in three additions, stirring until each batch has wilted and has been incorporated into the broth. Then add the peas and continue to cook, stirring occasionally, until the asparagus, peas, and spinach are just tender, 3 to 5 minutes more. The vegetables will continue to soften off the heat, so be careful not to overcook!
Finish with goat cheese and lemon zest. Remove the pan from the heat. Stir in the goat cheese and lemon zest until the cheese has broken down and the texture is creamy. If the pasta is too thick for your liking, stir in a few tablespoons of water to loosen it. Taste and season again with salt and pepper.
Garnish and serve. Divide the orzo among bowls and top each serving with parsley, mint, and grated Parmesan cheese, if you like.