Preheat the oven to 190°C. Line a baking tray with parchment paper and set it aside.
Gently wipe the mushrooms with a dry kitchen towel to remove any dirt. Do not rinse them with water, as mushrooms absorb moisture and this will affect the final texture.
Carefully remove the stems from each mushroom cap. Finely chop the stems and set them aside for the filling.
Arrange the mushroom caps hollow-side up on the prepared baking tray. Lightly brush or drizzle the inside of each cap with a small amount of olive oil.
In a mixing bowl, add the softened cream cheese and butter. Mix until completely smooth and creamy, ensuring there are no lumps.
Add the grated cheddar cheese, chopped mushroom stems, chopped onion, minced garlic, parsley, salt, black pepper, and dried oregano. Mix thoroughly until everything is evenly combined and well distributed.
Using a spoon, generously fill each mushroom cap with the cream cheese mixture, slightly mounding the filling on top without pressing it down too firmly.
In a small bowl, combine the breadcrumbs with the remaining olive oil. Sprinkle the breadcrumb mixture evenly over the tops of the filled mushrooms to create a light, crisp topping.
Place the tray in the preheated oven and bake for 18 to 22 minutes, or until the mushrooms are tender, the filling is hot throughout, and the tops are lightly golden.
Remove from the oven and allow the mushrooms to rest for 3 to 4 minutes before serving. This helps the filling set slightly while remaining creamy.