Place potatoes into a large roasting pan and drizzle with 2 tablespoons olive oil. Sprinkle with salt and mix to coat potatoes with salt and olive oil. Turn so the cut sides are up.
Roast in the preheated oven for 30 minutes.
While potatoes are cooking, pour 1 teaspoon olive oil into a large skillet over medium heat and cook pancetta, stirring often, in the hot oil until pancetta releases some fat and looks like cooked ham, about 5 minutes. Stir in king trumpet, chanterelle, nameko, and clamshell mushrooms, adding a pinch of salt as they cook.
Turn heat to high and cook mushrooms until most of the juices evaporate and mushrooms begin to brown, about 10 minutes.
Turn oven heat up to 425 degrees F (220 degrees C).
Stir potatoes in the baking dish; mix mushrooms and pancetta with potatoes. Return to oven and bake for 10 minutes; stir and continue baking until potatoes are browned, soft, and tender, about 10 more minutes. Let cool slightly, about 10 minutes.
Drizzle sherry vinegar over potatoes and mushrooms, sprinkle with tarragon, garlic, and 1 tablespoon olive oil, and toss to mix. Taste and adjust seasoning. Transfer to a serving platter.