Bring a pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving 1/2 cup of the cooking water.
While the pasta is working, in a large skillet, bring 2 inches of water to a boil, salt it, add the asparagus and cook for 3 minutes. Transfer the asparagus to a bowl of ice water to stop the cooking; drain and set aside. Reserve the skillet.
Using a food processor, puree 1/2 cup stock, the mint, parsley, pistachios and EVOO.
In the reserved skillet, melt the butter over medium heat. Add the shallots and garlic and cook, stirring, for 2 minutes; season with salt and pepper. Whisk in the flour. Stir in the wine and cook until reduced to 2 tbsp. Add the remaining 1 cup stock and cook until thickened, about 5 minutes. Lower the heat to low. Stir in the lemon juice (or vinegar). Remove from the heat and stir in the pistachio puree.
Add the pasta, asparagus and a handful of cheese to the skillet; toss, stirring in the reserved cooking water to thin the consistency if desired. Season with salt and pepper. Pass more cheese at the table.