Just put on a new coat of asphalt overtop ... and small stones. Now if
I could just remember what purpose those stones serve ???

Aha ... I knew this :-) ... "With conventional tar and gravel roofing
the tar is covered with a thin layer of gravel to protect the tar from
the harmful ultra violet rays of the sun. Contrary to popular belief it
is not water and rain that are responsible for the majority of the
damage to roofing products, it's the constant exposure to the sun
which, in the case of your type of roof, rob the tar of solvents which
cause it to become brittle, crack, or blister.

Another popular way to protect a built-up roof from the sun is with the
application of an aluminum coating in lieu of the gravel. However,
according to roofing experts this method doesn't offer the roof the
level of protection from the sun that gravel does. Unlike the gravel,
which will not deteriorate unless eroded by excessive wind and rain,
the aluminum coating will only last five to seven years before an
additional application is required where the conventional tar and
gravel roof should last somewhere in the neighborhood of fifteen years.
We suggest that you go with the gravel."

Ref ... http://www.onthehouse.com/qa/37