Preheat the griddle to medium heat for 10 minutes. Add oil to left side of griddle and spread around with spatula.
Add turkey and stuffing and cook, stirring occasionally, until warmed through, 4–5 minutes. Set aside.
Combine the mayonnaise and poultry seasoning in a small bowl, then spread over one side of each slice of bread.
Add the bread to the griddle, buttered side down. One each slice, add Gruyère and a few pieces of Brie.
Top 4 slices of bread with equal parts turkey, stuffing, and cranberry sauce. Using the melting dome, cook until the cheese has melted and the bread is golden brown, 4–5 minutes.
Flip the bread without the meat onto the bread with the meat. Using a griddle press, press down on the top of each sandwich for a few seconds. Remove from the griddle and serve.
