Heat the olive oil in a large frypan over medium heat. Stir in the garlic and onion and cook until the onion has softened and the garlic begins to brown, about 10 minutes. Stir in the thyme and portobello mushrooms, then turn the heat to low. Season to taste with salt and pepper and cook until the mushrooms have reduced but are not browning, 30 to 35 minutes.
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Cover and bring the water to a boil over high heat. Add the broccoli rabe, recover and steam until tender, about 6 minutes. Once the broccoli rabe has cooked, toss it with the mushroom mixture and sprinkle with Parmesan cheese to serve.