Once the darkest areas are shaded, I quickly add some more tone using an overhand grip and shading with the side of the 6b. Normally I use pencil-tip shading, but in this case I want the grainy look of side shading to suggest the texture of the eggshell.
I like to keep some drawn-line texture in my drawing, but I try to make sure that directional lines make sense, wrapping around the object or suggesting changes of plane - don't just shade at one random, meaningless angle across the whole surface.
If you prefer a more detailed, realist look, you'll need to take your time and be careful to make the edges of your shaded areas very soft, lifting the pencil off towards the end of the stroke. If you've applied too much pencil, use a kneadable eraser in a dabbing motion to lift, rather than rub, the graphite.