Step 1: Preheat your oven to 400°F (200°C). Wash the sweet potatoes thoroughly and pat them dry. Prick each potato several times with a fork.
Step 2: Rub each sweet potato with olive oil, then sprinkle generously with salt and black pepper. Place them directly on an oven rack or a baking sheet.
Step 3: Bake for 45-60 minutes, or until the sweet potatoes are tender when squeezed and easily pierced with a fork.
Step 4: Once baked, remove from the oven and let them cool slightly (about 10 minutes). Reduce the oven temperature to 375°F (190°C).
Step 5: Carefully slice each sweet potato lengthwise, about two-thirds of the way through, creating a boat shape but keeping the two halves connected. Scoop out most of the flesh into a large bowl, leaving a border of about 1/4 inch around the skin.
Step 6: To the scooped-out sweet potato flesh, add the softened butter, cream cheese, minced garlic, chopped fresh rosemary, and fresh thyme. Season with smoked paprika, salt, and pepper to taste.
Step 7: Mash the mixture until smooth and creamy. Taste and adjust seasonings as needed.
Step 8: Gently fold in about two-thirds of the grated cheddar cheese and half of the grated mozzarella cheese into the mashed sweet potato mixture. Reserve the remaining cheese for topping.
Step 9: Spoon the cheesy sweet potato filling back into the sweet potato skins, mounding it slightly.
Step 10: Arrange the stuffed sweet potatoes on a baking sheet. Sprinkle the remaining cheddar and mozzarella cheese evenly over the tops of each stuffed potato.
Step 11: Bake for another 15-20 minutes, or until the cheese is melted, bubbly, and golden brown.
Step 12: Garnish with extra fresh thyme or chives, if desired. Serve hot and enjoy!