I would just do it in photoshop with the Burn tool. Just set the brush to be very soft, and set the exposure for the tool low (maybe 10% to 20%). Then just paint in the shadow manually (and mask out the part of the letter that's supposed to be "higher" and not shadowed).

You can create paths which will held with the Burn process described above AND provide the outlines necessary to add the little green flourishes by outlining the type in a drawing program (like Illustrator or CorelDraw), converting the outline to curves, then cutting the outline path to remove the overlap with the letters themselves. The inner portion of the path provided the line segments needed to construct a perfect Burn mask for the letters themselves, and the outer portion can also be segmented, with the ball caps added for finish.

I don't know about 'best', but an easy way I have done exactly that is with a small shape in front of the lettering which is filled with a gradient, probably set to multiply (in illustrator for example). The effect is completed by a texture overlay, also set to some blending mode.