Preheat your oven to 450°F. While it heats, arrange the gnocchi and sliced mushrooms on a large sheet pan, spreading them in a fairly even layer. Add the smashed garlic cloves, drizzle with olive oil, and season generously with salt and pepper. Toss everything together to coat evenly—I like to use my hands to make sure each piece gets a light coating of oil, which ensures even roasting and browning. Cut the lemon in half and place the halves cut-side down directly on the pan, which will allow the lemon flesh to caramelize and release its oils into the pan.
Roast the sheet pan in the preheated oven for 15 minutes. During this time, the gnocchi will begin to develop a light golden color on the edges, the mushrooms will release their moisture and start to caramelize, and the garlic will soften and become fragrant. The lemon halves will char slightly and intensify in flavor. I like to use this time to prepare the asparagus so it's ready to go in right when the timer beeps.
Remove the pan from the oven after the initial 15 minutes and add the trimmed asparagus pieces, tossing them with the other ingredients to distribute evenly across the pan. Return to the oven and roast for an additional 8-10 minutes, until the asparagus is tender-crisp and the gnocchi has developed more color. The mushrooms should be well-browned and the lemon halves deeply caramelized.
While the pan finishes roasting, prepare a large serving bowl. When the pan comes out of the oven, carefully squeeze the roasted garlic cloves out of their skins directly into the bowl—they should be soft enough to slip right out. Squeeze the juice from both caramelized lemon halves into the bowl as well. Use a fork to mash the garlic and lemon together into a paste, which will create the foundation for your dressing and help distribute the flavors throughout the dish.
Add all the roasted contents from the sheet pan to the bowl with the lemon-garlic paste, including any oil that has collected on the pan. Gently toss everything together so the paste coats the gnocchi, mushrooms, and asparagus evenly. Stir in the dried oregano, fresh parsley, and freshly grated Parmesan cheese, tossing once more to combine. For freshly grated Parmesan, I always grate it just before serving—it melts more elegantly into the warm pasta and has a superior flavor compared to pre-grated cheese. Taste and adjust seasoning as needed before serving.