The best way to distribute cheese onto your bread for fast and even melting is to shred the cheese. However, for this hack, store-bought bags of shredded cheese won't cut it.
Store-bought bags of cheese have an anti-clumping agent that is completely okay to eat but prevents the cheese from melting properly when you add it to grilled cheese.
Buying pre-shredded cheese saves you a few minutes, but it often costs more than a block of cheese. You'll also find a difference in flavor when you shred cheese from a block.