Preheat the oven to 200 degrees Celsius. Finely mince the half onion and press the garlic clove. Clean the two large portobello mushrooms and carefully break or cut out the stems to make room for the filling. Finely chop the fresh oregano.
Heat the olive oil in a frying pan over medium-high heat. Briefly sauté the onion and garlic until translucent. Add the ground beef and cook until completely crumbly and brown. Stir the tomato paste and fresh oregano through the meat and let everything cook gently for a few more minutes.
Place the hollowed out portobellos side by side in a baking dish or on a baking sheet. Spoon the hot ground beef mixture into the mushrooms and distribute evenly. Sprinkle the grated pecorino over the meat and finish by distributing the pine nuts over the cheese.
Place the portobellos in the preheated oven and bake them until tender, about fifteen minutes. Remove the mushrooms from the oven once the cheese is completely melted and the pine nuts have turned slightly golden. Serve immediately.