Preheat oven to 400 degrees.: Begin by heating the oven until it reaches the correct temperature so the asparagus and tomatoes roast evenly and develop those pockets of caramelization, you will smell the oven warming and the air feel a touch dryer in the kitchen, which primes the vegetables to brown rather than steam, and a common issue is putting cold pans in too early which can delay browning and lead to limp texture.
Boil and drain pasta according to package directions, reserving 1/4 to 1/2 cup of the pasta water for last step. Meanwhile, place asparagus and halved tomatoes in an oven-safe skillet or baking sheet. Drizzle with olive oil and sprinkle with salt and pepper. Roast for about 15 minutes, until vegetables have browned in places and asparagus is tender. Remove from the oven.: While the oven heats, bring a pot of water to a rolling boil and add a generous pinch of salt , then cook the spaghetti until it is al dente, when you drain the pasta keep some of the starchy water as it acts like a binder, giving the pesto body and helping it cling to each strand, and avoid rinsing the pasta which would wash away that starch and cool the noodles.
While pasta and veggies are cooking, add 1-1/2 cups of spinach and pesto ingredients (except walnuts) to blender. Puree on high until a smooth consistency is reached. Add the walnuts and puree again until smooth (there can be some coarse walnut pieces remaining).: Arrange the cut asparagus and halved tomatoes in a single layer so they roast rather than steam, you should hear a faint sizzle as they hit the hot pan and notice edges browning and the tomato skins beginning to wrinkle, this browning develops savory depth, and be cautious of overcrowding which traps moisture and prevents caramelization.
Toss pesto and pasta together. Add to skillet with the veggies, tossing to combine the veggies. Heat over low heat until the sauce coating the pasta is warmed. Add 1/4 cup pasta water while heating. Add additional to keep pasta sauce creamy, if necessary.: Blend the spinach , garlic , parmesan , lemon juice, olive oil , and a little water to form a vivid green base, the smell will be herbaceous and slightly tangy, then adding walnuts creates a nutty richness and slight grain for body, and a pitfall here is over thinning the sauce which dilutes flavor so keep a balance between creamy and concentrated.
Once heated through, serve and enjoy!: At this stage the warm spaghetti meets the green pesto and roasted vegetables, stirring gently will create a glossy sauce that clings to the noodles, you will notice steam rising and a comforting meld of roasted and herby aromas, and if the mixture seems dry add the reserved pasta water in tablespoon amounts to reach a silky consistency, avoiding adding too much at once which can make the sauce watery.
Once heated through serve and enjoy: As you plate, the dish should glisten and release a mix of nutty, roasted, and bright citrus notes, take a moment to taste for seasoning and add a sprinkle of parmesan if you want more umami, and a frequent mistake is serving immediately without tasting which can leave the dish under seasoned.