In a skillet over medium heat, fry the bacon until it reaches a crisp texture. Transfer to a plate lined with paper towel to drain any excess fat.
Carefully pour off most of the rendered bacon fat from the pan, leaving a small amount behind for flavor. Add the butter and let it melt over medium-low heat.
Place both slices of bread in the pan. On one slice, layer the shredded cheddar followed by the cooked bacon. On the other, lay down the slices of processed cheese. Cover the skillet to trap heat and allow the cheese to melt thoroughly while the bread toasts to a golden brown on the underside.
Once the cheeses have melted, arrange the dill pickle slices over the bacon side and press both halves together to complete the sandwich.
Slice and serve immediately while hot.