You can make a normal pasta filata base, then pull off a chunk of the curd, stick your finger in it, but not through it to create an indentation, then make the indentation bigger to form a pouch, then scoop some cream inside and seal the pouch.
The cream inside can be made in various ways, depending on the style of burrata you want to make. You can use heavy full fat cream that will ooze, or you can whip it so it is lighter, or you can make a cultured cream, or you can even make a high-cream fresh curd, so it's coagulated.