Before, I suggest you a correct distillation apparatus/ procedure for oil extraction. One of the foremost question arises here is the quantity of plant material i.e., Ocimum. If you are working on lab scale level, then certainly you should go for Clevenger-type apparatus (hydro-distillation based apparatus), a commonly used glass based device popular among researchers throughout the World including India.
There are also microwave based distillation units available.
You may also try supercritical CO2 extraction as rightly mentioned by Dr Vladimir in his answer, if the unit is available near to you. Supercritical CO2 based distillation is quite convincing and time saving technique available till date.
Furthermore, for larger qualities such as 50/ 100 kg or more materials, steam based distillation shall be appropriate.
Unfortunately you present no information on how the essential oil is stored in the plant organ and whch plant organ it i really is. That would make the answer more simple. Methods are:
1. Hydrodistillation. Most used method, but because it works with heat and water, it can generate artifcts (see liiterature).
2. Extaction of the plant material (dried or fresh) with petrol. The extract, however, will contain most lipophilic constituents in aditin to the essential oil constituents.
3. CO2 extraction. This owever needs a special equipment, but will be the most modern and specific one.
4. When the essential oil is contained in surface located essential oil cells (e.g. as for the Lamiaceae) you may also spoil the surface with petrol until theoil is separated from the leaves. (this is a very special method but will give you the native essential oil).
Supercritical Fluid extraction has many advantages over other traditional methods, since you can control temperature and pressure, thus the density and affinity of your dissolvent over your compounds. Besides, allowing to conserve bioactivity of your desired molecules.
Perhaps the review in the link can be of your interest and help,
Steam distillation is the best. Although it will take time, but it is worth it.
Other upscale methods can be considered as already discussed in the thread.
Supercritical fluid extraction has many advantages compared to other traditional methods, since you can control (T, P) also making it possible to maintain the bioactivity of your desired molecules