Phase 1: Baking the Potatoes

1. Preheat Oven: Preheat your oven to 400°F (200°C). Position a rack in the center of the oven.
2. Prep Potatoes: Scrub the potatoes thoroughly under cold running water. Pat them completely dry with a paper towel. This is crucial for crispy skin.
3. Oil and Salt: Pierce each potato several times with a fork. This allows steam to escape during baking, preventing them from exploding. Drizzle the potatoes with olive oil and use your hands to rub it all over the skins. Sprinkle generously with coarse sea salt.
4. First Bake: Place the potatoes directly on the oven rack (for even crispier skins) or on a baking sheet. Bake for 60-75 minutes, or until the skins are crisp and the flesh is completely tender when pierced with a fork or skewer. Cooking time will vary depending on potato size.

Phase 2: Preparing the Savory Mushroom Filling

1. Sauté Aromatics: While the potatoes are baking (about 30 minutes before they’re done), start the mushroom filling. Heat 1 tablespoon of olive oil and 2 tablespoons of butter in a large skillet or pan over medium heat. Add the chopped onion and cook, stirring occasionally, until softened and translucent, about 5-7 minutes.
2. Cook Mushrooms: Add the minced garlic and dried thyme (if using fresh, add it later with the wine/broth) and cook for another minute until fragrant. Increase the heat to medium-high. Add the chopped mushrooms to the skillet. Spread them in a single layer as much as possible and let them cook undisturbed for 3-4 minutes to develop some browning. Then, stir and continue to cook until they have released their liquid, the liquid has evaporated, and the mushrooms are nicely browned and tender, about 8-10 minutes.
3. Deglaze (Optional): If using, pour in the white wine or vegetable broth to deglaze the pan, scraping up any browned bits from the bottom. Let it simmer and reduce for a minute or two. If using fresh thyme, add it now.
4. Season Mushrooms: Season the mushroom mixture generously with salt and freshly ground black pepper to taste. Remove from heat and set aside.

Phase 3: Creating the Creamy Stuffed Potato Filling

1. Cool and Scoop: Once the potatoes are baked, carefully remove them from the oven. Let them cool for about 10-15 minutes, or until they are cool enough to handle.
2. Halve and Scoop: Slice each potato in half lengthwise. Using a spoon, carefully scoop out the hot potato flesh into a large mixing bowl, leaving about a 1/4-inch thick shell of potato attached to the skin. Be gentle to avoid tearing the skins. Arrange the hollowed-out potato skins on a baking sheet.
3. Mash the Potato: To the bowl with the scooped potato flesh, add the softened butter, warmed milk/cream, and sour cream/Greek yogurt. Mash with a potato masher or a fork until smooth and creamy. Avoid overmixing, which can make the potatoes gummy.
4. Combine and Season: Add about half of the shredded cheddar cheese (1/2 cup) and all the Gruyère cheese to the mashed potato mixture. Stir in most of the chopped chives/green onions (reserving some for garnish).
5. Incorporate Mushrooms: Gently fold the sautéed mushroom mixture into the mashed potato mixture. Taste and adjust seasoning with salt, pepper, and a pinch of nutmeg if desired. The filling should be very flavorful.

Phase 4: Stuffing and Second Bake

1. Stuff the Skins: Spoon the mushroom-potato filling generously back into the potato skin shells, mounding it attractively.
2. Top with Cheese: Sprinkle the remaining 1/2 cup of shredded cheddar cheese over the top of the stuffed potatoes.
3. Second Bake: Return the baking sheet with the stuffed potatoes to the 400°F (200°C) oven. Bake for another 15-20 minutes, or until the filling is heated through and the cheese on top is melted, bubbly, and lightly golden brown.
4. Garnish and Serve: Carefully remove the stuffed baked potatoes from the oven. Let them cool for a few minutes. Garnish with the remaining fresh chives or green onions before serving hot.