The mechanism that causes the prompt-emission episode of gamma-ray bursts (GRBs) is still widely debated despite there being thousands of prompt detections. The favoured internal shock model relates this emission to synchrotron radiation. However, it does not always explain the spectral indices of the shape of the spectrum, often fit with empirical functions. Multi-wavelength observations are therefore required to help investigate the possible underlying mechanisms that causes the prompt emission. We present GRB 121217A, for which we were able to observe its near-infrared (NIR) emission during a secondary prompt-emission episode with the Gamma-Ray Burst Optical Near-infrared Detector (GROND) in combination with the Swift and Fermi satellites, covering an energy range of 0.001 keV to 100 keV. We determine a photometric redshift of z=3.1+/-0.1 with a line-of-sight extinction of A_V~0 mag, utilising the optical/NIR SED. From the afterglow, we determine a bulk Lorentz factor of Gamma~250 and an emission radius of R<10^18 cm. The prompt-emission broadband spectral energy distribution is well fit with a broken power law with b1=-0.3+/-0.1, b2=0.6+/-0.1 that has a break at E=6.6+/-0.9 keV, which can be interpreted as the maximum injection frequency. Self-absorption by the electron population below energies of E_a<6 keV suggest a magnetic field strength of B~10^5 G. However, all the best fit models underpredict the flux observed in the NIR wavelengths, which also only rebrightens by a factor of ~2 during the second prompt emission episode, in stark contrast to the X-ray emission, which rebrightens by a factor of ~100, suggesting an afterglow component is dominating the emission. We present GRB 121217A one of the few GRBs for which there are multi-wavelength observations of the prompt-emission period and show that it can be understood with a synchrotron radiation model.