Preheat the oven to 375 degrees F (190 degrees C).
Pierce sweet potatoes all over with a fork. Rub 1 tablespoon sea salt into potato skins. Place on a parchment-lined baking sheet.
Bake in the preheated oven until a sharp knife easily cuts into potatoes, 50 to 60 minutes. Remove from oven and allow to cool enough to handle, about 10 minutes. Leave the oven on; cut potatoes in half lengthwise.
Scoop out each potato half into a large bowl, making sure to keep the outer peel/shell intact. Mash the cooked sweet potato flesh thoroughly, until smooth, then add cream cheese, butter, brown sugar, 1 teaspoon salt, pepper, cinnamon, 1/8 teaspoon nutmeg, and ginger. Mix completely. Spoon filling into each potato skin. Place filled skins back onto the parchment-lined pan. Sprinkle with panko bread crumbs. Cut vegan Cheddar into strips and layer onto potatoes like lattice.
Bake in the preheated oven until potatoes are just beginning to brown, 10 to 12 minutes. Remove from oven; sprinkle with parsley and green onions. Bake for an additional 3 to 5 minutes. Sprinkle with remaining nutmeg prior to serving.