smut on oak leaf holly leaves
The black coating looks like sooty mold. It indicates that you have a sucking insect on your oak holly. The insect, likely a soft scale, sucks plant sap and then produces honeydew which drops on the leaves below, which then grows sooty mold.
To find the insect (which looks nothing like most insects) look on the underside of the leaves above where you see sooty mold. You would see 1/8" ovals, perhaps with white, cottony-waxy ovisacs.
You may not need to do anything if there aren't a great deal there, and beneficial insects provide control of many scale infestations. To protect beneficials, avoid spraying with insecticides during the summer.
If there is a great deal of sooty mold and treatment is necessary, spray the tree with a dormant rate of horticultural oil during the dormant season to control overwintering scales.
Also keep trees and shrubs watered during droughty periods and do not overfertilize.