Why my banana sauce is not smooth? here is my recipe

100g  banana
* 1 egg
* 1 tbsp. corn starch
* 3 tbsp. granulated sugar
* 150ml milk

I use folk to beat bananas. Then put everything together and then strain. then put it on stove and do double bowl. After the sauce becomes thick. It looks like this: 

It is not so smooth in texture and when I eat it I can feel something like small fibers from bananas. What technique you suggest me to make it more smooth? I have consider two main ways, first make the fibers to become very very small by using blender. second do not let the finer comes out of the banana by don't beat it too much by using folk.

Should I use blender to make it very very smooth? or I should use folk but beat just a little bit to prevent the finer to come out?

What technique you suggest me? what about the portion of milk and corn starch, is it also effect the smooth or not smooth texture? if I place the bowl too long on stove, is it gonna give bad texture not smooth?
A blender certainly sounds like the easiest method.

If you prefer straining, but your sieve isn't fine enough to filter out the things you don't like, use cheesecloth. You can use enough layers to get a really fine strain, though bananas are thick enough that you'll have to squeeze it through.

The other thing you can try for things like this is a food mill, with the finest disk you have, but it sounds like you don't even want tiny tiny particles, so that may not be good enough for you - and it takes a bit of time and elbow grease.