Preheat the oven to 400 degrees F.

Wrap each potato in aluminum foil and bake until fork-tender, 1 ¼ to 1 ½ hours. Set aside until cool enough to handle.

While the potatoes are cooling, heat a skillet over medium-high heat and add the andouille. Cook, stirring frequently, until the sausage has rendered some of its fat and is lightly golden with some crispy edges but not dry, about 3 minutes. Add the garlic and cook until fragrant, 1 minute longer. Transfer to paper towels to drain. 

Cut each potato in half lengthwise. Scoop out the pulp with a melon baller or small spoon, leaving a 1/4-inch border of potato pulp next to the skin. Return the potato shells to the baking sheet. 

Put the scooped potato pieces in a mixing bowl and mash with a fork until smooth. Combine the two cheeses in a small bowl and toss to blend. Add 2 cups of the cheese, the green onions, heavy cream, sour cream, and butter to the mashed potatoes and stir to combine. Fold in the andouille-garlic mixture and season with the salt and pepper. Add more cream if the mixture seems too dry.

Season the potato shells lightly with salt and pepper and then stuff the cavities with the potato mixture. Sprinkle the tops of the potatoes with the remaining cheese. Potatoes may be made up to this point several days in advance and refrigerated until ready to warm them on the grill.

Preheat a grill to medium-low, about 400 degrees F. 

Place the potatoes in a shallow grill proof baking dish and place the dish directly on the grill. Close the grill lid and cook until the cheese on top is golden and bubbly, and the potato is warmed through, 20 to 25 minutes. Serve hot.