You can touch it up with high-gloss black paint and a tiny brush (don't use a marker, wrong sheen). It will be better, but not perfect, and very inexpensive.
Otherwise, hire someone to rebuild the damaged corner with epoxy, not wood putty (JB Weld works well for this), sand, and respray at least the 4 visible sides of the cabinet. This will make it look like new, but likely cost a couple hundred.
Anything in between is likely to prove some combination of disappointing and expensive.
Good luck, and let us know how it turns out!