Preheat the oven to 425 degrees F.

Trim the ends of the onions, leaving the skins on, and cut them in half horizontally. Put the onions, cut-side up, in a baking dish just large enough to hold them in a single layer. Drizzle with 3 tablespoons of the oil; scatter the thyme sprigs over the top and season with salt and pepper. Add 2 cups of water, cover with foil, and bake for 1 hour. Remove the foil and bake, basting with the pan juices until the edges of the onions are browned, about 45 minutes to 1 hour more. (Add more water if pan is running dry.) Remove from the oven and cool.

Smash the garlic clove with the side of a cook's knife. In a large skillet, heat 2 tablespoons of the oil over medium heat, add the garlic and stir until golden, about 3 minutes. Remove the garlic and discard. Working in batches, add the spinach, stirring to wilt before each addition. When all the spinach has been added, raise the heat to high, season with salt and pepper, and stir to combine. Cover and cook until fully wilted, about 3 minutes. Remove from the heat and drain the spinach in a colander. When cool enough to handle, squeeze as much liquid from the spinach as possible and coarsely chop.

Lower the oven heat to 350 degrees F.

Scoop out the center of each onion, leaving at least half an inch of the outer rings, to make onion "bowls". Coarsely chop half of the onion centers, and reserve the remaining for another use. In a mixing bowl combine the chopped onion, spinach, lemon zest, eggs, cayenne, breadcrumbs, chopped thyme, and feta cheese. Season with salt and pepper. Divide the mixture evenly among the scooped-out onions. Drizzle the tops with the remaining olive oil and bake for 30 minutes. Serve hot or at room temperature.