Preheat your oven by positioning a rack in the upper third and setting it to broil.
Spread the mushrooms, eggplant, and diced onion across an unlined baking sheet. Place the garlic cloves, still in their skins, on a small piece of foil. Drizzle two tablespoons of olive oil over the vegetables and the garlic. Seal the foil around the garlic and place it on the sheet alongside the vegetables. Toss the vegetables to evenly coat in the oil and sprinkle with salt.
Broil the vegetables on the top rack, stirring halfway through, until they are lightly charred and caramelized around the edges, about 8 to 12 minutes. Keep a close watch as broiling times can vary.
Lower the oven temperature to 425°F (220°C) to prepare for baking.
Unwrap the foil and allow the garlic to cool slightly. In a food processor, combine the roasted mushrooms, eggplant, and onion along with the oats, parsley, nutritional yeast, tamari, oregano, and black pepper. Peel the garlic cloves and mash them into a paste using a fork, then add it to the food processor. Pulse the mixture until finely chopped but not fully puréed—small flecks of parsley should remain visible. Add the panko breadcrumbs and pulse briefly until incorporated.
Using a 3-tablespoon scoop, portion the mixture onto a parchment-lined baking sheet. You should form about 20 meatballs. With slightly damp hands, roll each portion into a smooth, even ball. Brush the tops generously with the remaining two tablespoons of olive oil.
Bake the meatballs on the upper rack for 25 to 30 minutes, or until they are firm and deeply golden.
Serve hot with warm marinara sauce, a sprinkle of parsley, and grated Parmesan if desired. Garlic bread on the side makes a perfect accompaniment for dipping.