Lay the pickle slices on a paper towel and pat them completely dry.
In a small bowl, stir together the softened cream cheese, garlic powder, and fresh dill. Spread this mixture evenly over one side of both bread slices.
Layer one slice of sharp cheddar on top of the cream cheese spread on the bottom slice. Arrange the dried pickle chips in a single, overlapping layer, then sprinkle the shredded mozzarella or Jack on top. Close with the second slice of bread.
Spread a thin layer of mayonnaise (or softened butter) on the outside top and bottom of the sandwich.
Heat a skillet or cast-iron pan over medium-low heat. Place the sandwich in the pan and cook for 3 to 4 minutes per side, pressing down gently with a spatula, until the bread is deeply golden brown and the cheese is fully melted.
Remove from heat, let sit for 1 minute to set, slice in half, and serve hot.