  Aims: We present a detailed view of the pulsar wind nebula (PWN) HESS
J1825-137. We aim to constrain the mechanisms dominating the particle transport
within the nebula, accounting for its anomalously large size and spectral
characteristics. Methods: The nebula is studied using a deep exposure from over
12 years of H.E.S.S. I operation, together with data from H.E.S.S. II improving
the low energy sensitivity. Enhanced energy-dependent morphological and
spatially-resolved spectral analyses probe the Very High Energy (VHE, E > 0.1
TeV) gamma-ray properties of the nebula. Results: The nebula emission is
revealed to extend out to 1.5 degrees from the pulsar, ~1.5 times further than
previously seen, making HESS J1825--137, with an intrinsic diameter of ~100 pc,
potentially the largest gamma-ray PWN currently known. Characterisation of the
nebula's strongly energy-dependent morphology enables the particle transport
mechanisms to be constrained. A dependence of the nebula extent with energy of
R $\propto$ E^\alpha with \alpha = -0.29 +/- 0.04 (stat) +/- 0.05 (sys)
disfavours a pure diffusion scenario for particle transport within the nebula.
The total gamma-ray flux of the nebula above 1~TeV is found to be (1.12 +/-
0.03 (stat) +/- 0.25 (sys)) $\times 10^{-11}$ cm$^{-2}$ s$^{-1}$, corresponding
to ~64% of the flux of the Crab Nebula. Conclusions: HESS J1825-137 is a PWN
with clear energy-dependent morphology at VHE gamma-ray energies. This source
is used as a laboratory to investigate particle transport within middle-aged
PWNe. Deep observations of this highly spatially-extended PWN enable a spectral
map of the region to be produced, providing insights into the spectral
variation within the nebula.
