Can you get access to the void from either end? If you can, you may be
able to slide in sheet PU insulation (e.g. Kingspan). This needs to be
of a depth to not adversely affect air circulation between the joists.
If not, then battening and plasterboard is probably the answer,
although there's better insulators to use than glasswool where the
depth is limited.

Injection into the void - bad. There needs to be air circulation
between ceiling and roofing to keep the joists dry and remove any
rainwater blown under the tiles/slates as well as moisture penetrating
from inside the kitchen.