Heat the olive oil in a frying pan. Add the chopped onion and cook over medium-low heat until softened.
Meanwhile, drain the mushrooms (reserve the soaking water). Discard the stalks.
Roughly chop the mushroom caps. Add to the pan. Sprinkle with salt and pepper. Cook for another minute.
Add the garlic. Cook, stirring, for about a minute.
Transfer the contents of the pan to a blender. Add the water in which the mushrooms were soaked. Pulse a few times to grind the mushrooms coarsely.
Heat the frying pan. The bottom is already coated with oil so there is no need to add any. Cook the ground meat over high heat, stirring to break up any lumps, until lightly browned.
Add the tomato paste and oregano to the pork. Sprinkle with salt and pepper. Cook, stirring, for a few minutes or until the pieces of pork has absorbed the color of the tomato paste.
Pour in the mushroom mixture, including the liquid, and stewed tomatoes. Stir. Taste. Add more salt and pepper, as needed, and a bit of sugar to balance the acidity of the tomato paste. Bring to the boil, cover and simmer for 20 to 30 minutes until thickened. A minute before turning off the heat, stir in the basil leaves and adjust the seasonings one last time, if needed.
Toss the cooked spaghetti with the sauce. Transfer to a serving platter or tray. Top with shredded cheese. Sprinkle with chopped parsley. Serve.