Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper for easier cleanup.
Scrub the sweet potatoes well and pat them dry. Pierce each sweet potato several times with a fork to allow steam to escape while baking.
Place the sweet potatoes on the prepared baking sheet. Drizzle with 1 tablespoon of olive oil and rub it over the skins to coat evenly. Bake for 40 to 45 minutes, or until the sweet potatoes are tender when pierced with a knife.
While the sweet potatoes bake, prepare the creamy mushroom and spinach filling. Heat the remaining 1 tablespoon of olive oil and the butter in a large skillet over medium heat until the butter melts and begins to foam slightly.
Add the chopped yellow onion to the skillet and cook for 3 to 4 minutes, stirring often, until the onion softens and turns translucent.
Stir in the minced garlic and cook for 30 seconds to 1 minute, just until fragrant, being careful not to let it brown.
Add the sliced cremini mushrooms to the skillet. Cook for 6 to 8 minutes, stirring occasionally, until the mushrooms release their moisture and most of the liquid has evaporated and the mushrooms begin to brown.
Season the mushroom mixture with the fine sea salt, black pepper, and dried thyme. Stir well to coat the vegetables evenly with the seasonings.
Add the fresh baby spinach to the skillet in batches if needed. Cook, stirring, for 2 to 3 minutes, until the spinach wilts down and mixes with the mushrooms and onions.
Reduce the heat to low and pour in the heavy cream. Stir to combine and let the mixture simmer gently for 2 to 3 minutes, until slightly thickened and creamy.
Sprinkle in the grated Parmesan cheese and stir until it melts into the sauce and the filling looks smooth and creamy. Taste and adjust the seasoning with a little more salt and pepper if needed.
When the sweet potatoes are tender, remove them from the oven and let them cool for 5 minutes, just until they are easier to handle.
Using a sharp knife, carefully slice each sweet potato lengthwise down the center, without cutting all the way through. Gently press the ends toward each other to open the potatoes and create space for the filling.
Use a fork to lightly fluff the inside of each sweet potato, keeping the flesh inside the skin to form a base for the filling.
Spoon the creamy mushroom and spinach mixture evenly into the opened sweet potatoes, dividing it among the four potatoes.
Sprinkle the stuffed sweet potatoes with the chopped fresh parsley if using, and serve warm.