If fresh oyster mushrooms aren't available, you can use stemmed chantarelles or shiitakes, or very thinly sliced stem-on king oysters or portobellos. Timings will vary depending on the mushroom variety and age (dryness).
Preheat oven to 350°F. Line a large baking sheet with parchment paper.
Stem mushrooms and gently wipe clean as needed with a paper towel. Combine oil, maple syrup, soy sauce, smoked paprika, black pepper, and salt in a large bowl. Add mushrooms and toss gently to coat. Arrange on prepared baking sheet.
Roast mushrooms until lightly browned around the edges and slightly crisp, turning once or twice, about 25 minutes. Shut off oven, leaving mushrooms inside. Let cool in oven until mushrooms are evenly crisp-chewy, about 30 minutes. Remove and let cool completely. (Store in an airtight container in the fridge up to 1 week. To reheat, warm in a skillet over medium-low heat or microwave until just sizzling, 30 seconds to 1 minute.)