In a small bowl, whisk together the miso, lemon juice, and Dijon mustard. If you can't get the miso lumps out, just add a splash of hot water from the tap and whisk again. Set this mixture aside.
Place a deep skillet or braiser-style pot over medium heat. Once the pot is hot, pour in 1 teaspoon of olive oil and swirl it around. Add the asparagus and season with salt and pepper. Sauté asparagus until bright green and slightly tender, about 2 minutes. Transfer the cooked asparagus to a plate and return the pot to the stove.
Pour another teaspoon of olive oil into the pot and stir it around. Add the mushrooms to the pot and let them sit for 1 full minute. Stir them up and let them sit for another full minute. Season the mushrooms with salt and pepper and keep sautéing until slightly browned and tender, another minute. Transfer the cooked mushrooms to the plate with the asparagus.
Give the pot a quick wipe and return it to the stove over medium heat. Pour in the remaining olive oil and swirl it around. Add the leeks and stir. Sauté the leeks until very tender, about 3 minutes. If they begin to brown on the edges, lower the heat.
Add the capers, garlic, nutritional yeast, and chillies (if using) to the pot and stir. Keep stirring until very fragrant, about 30 seconds. Season with salt and pepper.
Add the orzo to the pot and stir to coat in the leeks and seasoning.
Add the vegetable stock, the non-dairy cream, and saffron to the pot and stir. Bring the orzo to a boil and then lower the heat to a simmer. Cook until the orzo is plumped up and a lot of the liquid is absorbed, about 10-11 minutes. I recommend stirring pretty much constantly as the orzo does tend to stick to the bottom of the pot.
Stir the peas, fresh dill, cooked asparagus, and mushrooms into the orzo. Also add the reserved miso, lemon juice, and Dijon mustard mixture. Keep stirring as the orzo simmers for another minute. Taste for seasoning one more time. If you find that the orzo is sopping up the liquid too quickly, just add a few splashes of water to "cream" it back up.
Serve the orzo hot with vegan "parmesan" on top if you like.