Preheat oven to 400°. Separate mushrooms into small clusters (or if single caps, thickly slice). Pile onto a rimmed baking sheet, drizzle with olive oil, and season with salt and pepper. Add thyme and toss to coat well. Roast in a single layer until sizzling and browned on the edges, about 15 minutes, turning once halfway through cooking.
Put shallot, a couple of pinches of salt, a few grinds of pepper, and the vinegar in a small bowl. Let sit 10 minutes to soften and mellow the shallot. Add hazelnut oil and whisk vigorously.
Slice endive crosswise and put in a serving bowl with lettuce and parsley. Season lightly with salt and toss to mix. Add hot roasted mushrooms and vinaigrette and toss gently but thoroughly. Top with manchego curls and hazelnuts.
*Find mushrooms at farmers' markets and well-stocked grocery stores; roasted hazelnut oil is available at such stores too.
TIPS FOR COOKS Shop: Regardless of variety, all mushrooms should smell sweet and earthy and have dry, firm, undamaged caps. If they're spongy or sticky, steer clear. Store: Keep in a paper bag (storing them in plastic rots them), chilled, up to 4 days. Even if they become completely dry, they'll be fine in stews; the juices plump them back up. Clean: Wipe with a barely damp paper towel. If they're very dirty or sandy, swish briefly in cold water and scrub with a small brush, then dry immediately (they get soggy fast). To cook or not to cook?: Most experts advise cooking all edible mushrooms because, to varying degrees (and depending on the person), they're difficult to digest raw. Also, many have toxins that cooking destroys. However, there's no conclusive proof that eating mild raw mushrooms, especially in moderation, is harmful.