Context. Accretion at planetary-mass companions (PMCs) suggests the presence of a protoplanetary disc in the system, likely accompanied by a circumplanetary disc. High-resolution spectroscopy of accreting PMCs is very difficult due to their proximity to bright host stars. For well-separated companions, however, such spectra are feasible and they are unique windows into accretion. Aims. We have followed up on our observations of the 40-Myr, and still accreting, circumbinary PMC Delorme 1 (AB)b. We used high-resolution spectroscopy to characterise the accretion process further by accessing the wealth of emission lines in the near-UV. Methods. We have used the UVES spectrograph on the ESO VLT/UT2 to obtain R_λ ≈ 50 000 spectroscopy, at 3300–4520 Å, of Delorme 1 (AB)b. After separating the emission of the companion from that of the M5 low-mass binary, we performed a detailed emission-line analysis, which included planetary accretion shock modelling. Results. We reaffirm ongoing accretion in Delorme 1 (AB)b and report the first detections in a (super-Jovian) protoplanet of resolved hydrogen line emission in the near-UV (Hγ, Hδ, Hϵ, H8, and H9). We tentatively detect H11, H12, He I, and Ca II H/K. The analysis strongly favours a planetary accretion shock with a line-luminosity-based accretion rate of Ṁ = 2 × 10⁻⁸ M_J yr⁻¹. The lines are asymmetric and are well described by sums of narrow and broad components with different velocity shifts. The overall line shapes are best explained by a pre-shock velocity of v₀ = 170 ± 30 km s⁻¹, implying a planetary mass of M_P = 13 ± 5 M_J, and number densities of n₀ ≳ 10¹³ cm⁻³ or n₀ ∼ 10¹¹ cm⁻³. The higher density implies a small line-emitting area of ∼1% relative to the planetary surface. This favours magnetospheric accretion, a case potentially strengthened by the presence of blueshifted emission in the line profiles. Conclusions. High-resolution spectroscopy offers the opportunity to resolve line profiles, which are crucial for studying the accretion process in depth. The super-Jovian protoplanet Delorme 1 (AB)b is still accreting at ∼40 Myr. Thus, Delorme 1 belongs to the growing family of ‘Peter Pan disc’ systems with (a) protoplanetary and/or circumplanetary disc(s) far beyond the typically assumed disc lifetimes. Further observations of this benchmark companion and its presumed disc(s) will help answer key questions about the accretion geometry in PMCs.