Either use sliced cheese, or hand shred the cheese. Pre-shredded cheese is coated (usually with starch or cellulose) to prevent it from clumping, but that also prevents the melted product from getting that nice, gooey, stretchy effect. Same goes for pizza.

Want to hear heresy?
Microwave it. It’s a different type - more chewy. But it takes 60 s

I mean I would demolish the quesadilla in the picture already, so keep doing that