Preheat the griddle to medium heat for 10 minutes. Squeeze about 1 tablespoon of oil onto the left side of the griddle, spreading it around with a spatula. 
Add the pulled pork and cook, stirring occasionally, until warmed through, 4–5 minutes; set aside.
Combine the butter, mayonnaise, and BBQ rub in a small mixing bowl, then spread the mixture over one side of each slice of bread.
Add the bread to the griddle, buttered side down. On each slice of bread place 1 slice of cheddar and one slice of Havarti.
Top 4 slices of bread with the pulled pork, and pickle. Cook until the cheese is melted and the bread is golden brown, 4–5 minutes.
Flip the bread without the pork onto the bread with the pork. Use a spatula or grill press to press the top of each sandwich for a few seconds. Remove the sandwich from the heat and let them rest for 2–3 minutes before serving.
