Set oven. Adjust a rack to the top third of the oven and preheat the oven to 375°F.
Cook onions, garlic and thyme. Coat the bottom of a large sauté pan with olive oil and place it over medium-high heat. Add the onions and cook, stirring frequently until they are soft and beginning to brown, about 10 minutes. Then stir in the garlic and thyme, and cook for another minute or so.
Add and cook mushrooms. Add the mushrooms, and stirring every minute or so, sauté until they are golden brown, about 15 minutes. (This will happen in a few stages -- first the mushrooms will soften, then they will loose some liquid, and once all of the liquid has reduced, they will begin to brown.)
Deglaze and season. Pour in the sherry, turn the heat to high and use a wooden spatula to scrape any bits of mushroom and onion that are stuck to the bottom of the pan. Reduce the sherry completely. Season to taste with salt and pepper. (Here's How.)
Add peas and spinach. Turn the heat to low, add the black-eyed peas and spinach, and stir to blend. Once the spinach has wilted, mix in ¼ cup of the Parmesan and season again with salt and pepper to taste.
Assemble. Pour the entire mixture into an (approximately 9 X 13 X 2 inch) baking pan. (You can use a deeper, smaller pan, too.)Sprinkle the remaining ¼ cup of Parmesan and the bread crumbs evenly over the top surface. Bake. Bake in the preheated 375°F oven until the top becomes golden brown and it's sizzling a bit along the edges, about 25 minutes. If it's not golden brown after 25 minutes, place it under the broiler for about 30 seconds. And if it seems like it's becoming too dark before the cooking time has finished, loosely lay a piece foil over the top.Serve!