It is best to build all of your sandwiches before you start cooking them, as it doesn't take long for them to cook.
Preheat griddle to medium heat.
Combine softened butter with everything seasoning. Spread on one side of each piece of bread.
Build each sandwich starting with bread (butter side out), 2 slices of cheddar cheese, 3-4 slices of pastrami, 2 slices of swiss cheese, and bread (butter side out). Repeat with remaining sandwiches.
Line out sandwiches on griddle top. Cover with lid or dome and let cook for 5 minutes. Remove lid/dome and flip each sandwich. Cook another 5 minutes and remove from griddle.