The shadow gap is left as a gap on purpose. It provides room for you to install your shutter frame and ensure the shutters operate correctly. It also disguises any out of level windows or bumps in the plaster.
If you use filler, there are 3 different colours to worry about: the wall colour, the shutter colour and the filler colour. Even if they are all white, they can be different shades of white. In time the filler can crack and discolour and just because you fill the gap it doesn’t make your shutter frame look square, your window will still be out of level.
The simple professional solution is to leave the gap as a shadow gap: the shutters look far neater and the shadow enhances the shutter frame.
A shadow gap will never discolour, crack or shrink, so your shutters will always look perfect.