We observed the slowly revolving pulsar 1E 161348–5055 (1E 1613, spin period of 6.67 h) in the supernova remnant RCW 103 twice with XMM-Newton and once with the Very Large Telescope (VLT). The VLT observation was performed on 2016 June 30, about a week after the detection of a large outburst from 1E 1613. At the position of 1E 1613, we found a near-infrared source with K_s = 20.68 ± 0.12 mag that was not detected (K_s > 21.2 mag) in data collected with the same instruments in 2006, during X-ray quiescence. Its position and behavior are consistent with a counterpart in the literature that was discovered with the Hubble Space Telescope in the following weeks in adjacent near-IR bands. The XMM-Newton pointings were carried out on 2016 August 19 and on 2018 February 14. While the collected spectra are similar in shape between each other and to what is observed in quiescence (a blackbody with kT ∼ 0.5 keV plus a second, harder component, either another hotter blackbody with kT ∼ 1.2 keV or a power law with photon index Γ ∼ 3), the two pointings caught 1E 1613 at different luminosity throughout its decay pattern: about 4.8 × 10³⁴ erg s⁻¹ in 2016 and 1.2 × 10³⁴ erg s⁻¹ in 2018 (0.5–10 keV, for the double-blackbody model and for 3.3 kpc), which is still almost about ten times brighter than the quiescent level. The pulse profile displayed dramatic changes, apparently evolving from the complex multi-peak morphology observed in high-luminosity states to the more sinusoidal form characteristic of latency. The inspection of the X-ray light curves revealed two flares with unusual properties in the 2016 observation: they are long (∼1 ks to be compared with 0.1–1 s of typical magnetar bursts) and faint (≈10³⁴ erg s⁻¹, with respect to 10³⁸ erg s⁻¹ or more in magnetars). Their spectra are comparatively soft and resemble the hotter thermal component of the persistent emission. If the flares and the latter component have a common origin, this may be a spot on the star surface that is heated by back-flowing currents that are induced by a magnetospheric twist. In this hypothesis, since the increase in luminosity of 1E 1613 during the flare is only ∼20%, an irregular variation of the same order in the twist angle could account for it.