Heat the oven and prepare the spaghetti squash. Preheat the oven to 400°F. Carefully cut off the top and bottom of the squash then cut the spaghetti squash lengthwise from top to bottom. Scoop out the seeds from each half. Drizzle with olive oil and sprinkle with salt and pepper. Place the halves cut side down on a parchment-lined baking sheet and roast for 35 to 45 minutes, or until the flesh pulls away in tender strands when scraped with a fork. Let it cool until it is safe to handle, then pull the squash into strands and set aside.. Prepare the mushrooms while the squash roasts. Gently wipe the portabellas clean with a damp paper towel. Twist out the stems. Use a spoon to scrape out the dark gills if you prefer a lighter-looking filling. Brush both sides lightly with olive oil and place the caps open-side down in a rimmed baking pan.
Roast the mushroom caps. When the squash comes out, keep the oven at 400°F. Roast the mushrooms for about 10 minutes, turn them open-side up, and roast 8 to 10 minutes more. They should look slightly softened and release some liquid. Carefully pour or blot away that liquid so the filling does not become watery.
Cook the onion. Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the chopped onion and cook for 3 to 4 minutes, stirring often, until it looks translucent, which means softened and slightly see-through.
Add the tomatoes. Stir in the chopped tomatoes and cook for about 3 minutes. They should soften and release enough juice to lightly coat the bottom of the pan.
Add the spaghetti squash. Add the cooked squash strands to the skillet and toss until the vegetables are evenly combined. Cook for 1 to 2 minutes, just until heated through. Season with salt and black pepper to taste.
Wilt the greens. Remove the skillet from the heat. Stir in the spinach, kale, and chard mix. The greens will soften from the heat of the filling. If the mix includes sturdy kale or chard pieces that stay firm, return the pan to low heat for 1 to 2 minutes.
Fill the mushroom caps. Divide the squash mixture evenly among the four roasted portabellas. Do not pack the filling down tightly. Sprinkle each cap with mozzarella, then top each with 1 tablespoon panko.
Bake until melted and crisp. Return the stuffed portabellas to the oven for 10 to 12 minutes, or until the cheese is melted and the panko is lightly golden. If you want deeper browning, broil for 30 to 60 seconds while watching closely.
Cool briefly and serve. Let the mushrooms rest for about 5 minutes. They will be very hot and may release a little more juice as they sit.