How do people use mozzarella cheese with fungi? Any alternatives to Mozzarella?

I tried cooking a cheese mushroom and babycorn dish.

Took butter melted it, added a dash of olive oil to stop the butter from burning.

Added half a clove of garlic to the sizzling bubbling oil/butter mix.

Lowered the heat to infuse the oil with garlic flavour while lightly browning the garlic clove shreds.

Added a little flour to it, and cooked it till it was graingy and brown.

Added milk to it while whisking continuously.

Flavoured it with salt to taste, oregano and finally half a block of Mozzarella cheese ~100 grams.

Then when the cheesy strings could be seen I added the broiled mushroom (button) and diced babycorn.

Tasted well, would certainly make it again for a quick snack.

Quick question, what are the alternatives to mozzarella and is there a way to make it at home SUCCESSFULLY?

Thanks for reading & forbyour time!

P.S. I know the food doesn't look good or appealing but the proof of the pudding is in eating! Not good at photography in general or dishes in particular.