Heat the oil over medium heat in a large, straight-sided sauté pan or large pot.
Add the shallots, 1 teaspoon salt, and 1/2 teaspoon pepper. Cook, stirring often, until the shallots are starting to soften, 4-6 minutes.
Add the asparagus, pasta, water, and peas (see note about timing and vegetable doneness). Cover and bring to a boil.
Reduce heat to a gentle simmer and cook, stirring here and there, until the pasta is just tender, 11-14 minutes.
Remove from the heat when there's still a little water left – you're looking for just enough to create a sauce. Stir in the lemon juice and zest, parmesan cheese, butter, and tarragon, and season with remaining 1/2 teaspoon salt and 1/4 teaspoon pepper.
Two Healthy Kitchens' Notes About This Recipe:
Parmesan Cheese: To make this pasta recipe truly vegetarian, be sure to select a parmesan cheese made with non-traditional enzyme alternatives from microbes or fermentation, rather than the traditional rennet.
Cooking the vegetables: You can control the doneness of the peas and asparagus, depending on the point in the cooking process when you choose to add them. Lindsay's recipe, as written in her Healthyish cookbook, directs you to add the asparagus and peas at the same time as the pasta. This works great, but because we sometimes prefer our veggies a bit more al dente, I found during our tests of this recipe that I prefer to wait and add my asparagus and peas just a little bit later. If that's also your preference, I would suggest bringing the pasta to a boil as directed, and then adding the veggies after the pasta has been simmering for 3-5 minutes (again, depending on how you like your vegetables cooked).
Make-ahead options: You can certainly complete some steps of this recipe ahead of time, such as slicing your shallots and asparagus. In addition, this skillet meal reheats nicely, so if you know you'll be rushed at dinnertime, you can actually make this recipe in its entirety earlier in the day or the day before. If you want to try this, I would recommend slightly undercooking the asparagus and peas at first, so they don't become overcooked when you reheat the pasta (see note above about cooking the veggies). Also, if you'd like to loosen the pasta a bit upon reheating and regain some of the silkiness the light sauce has when it's first hot off the stove, you can add a small splash of olive oil or broth as you reheat.