1 pound mixed mushrooms, such as button, cremini, shiitake, oyster, chanterelle or porcini
1 bunch medium asparagus, about 20 spears
3 tablespoons extra-virgin olive oil
10 fresh sage leaves, chopped
1 tablespoon fresh thyme leaves, chopped
1/2 teaspoon kosher salt, or as needed
Freshly ground pepper
10 cloves garlic
1 cup chopped green onions
1 pound mostaccioli
1/2 cup fresh Italian parsley leaves, chopped
1/2 cup freshly grated grana Padano
Heat the oven to 450 degrees, with two rimmed baking sheets on the bottom rack. (If your oven is not large enough to fit two pans on one rack, you can put one on the top and one on the bottom and rotate halfway through the cooking time.)
Heat a large pot of well-salted water to a boil for pasta. Wipe the mushrooms clean. Discard the stems. Cut the mushrooms into large chunks. Snap off the woody bottom stems of the asparagus and peel the lower half of the remaining tender stems. Cut the asparagus on the bias to about the same length as the mostaccioli.
In a large bowl, toss the mushrooms with 1 tablespoon olive oil and half the sage and thyme. Season with salt and pepper to taste. Roast on one sheet pan until the mushrooms are browned and tender, tossing once or twice, 18 to 20 minutes. In the same bowl, toss the asparagus and garlic with another 1 tablespoon olive oil and remaining sage and thyme. Season with salt and pepper to taste. Roast on the second pan until the asparagus is golden and tender, and the garlic is soft, about 10 minutes. Move both pans to the stove top to keep warm.
Add the mostaccioli to the boiling water. Meanwhile, in a large skillet over medium heat, add the remaining 1 tablespoon olive oil. Add the green onions and cook until wilted, about 3 minutes. Add the roasted garlic and mash with a wooden spoon. Season with salt and pepper to taste; add 1 cup pasta water. Heat to a simmer and cook until the garlic breaks down in the sauce, about 3 minutes.