A state-of-the-art anode-supported Ni-YSZ/YSZ/GSC/LSC SOFC with 16 cm2 cathode area was tested at low anodic flow rate (6.25 Ncc min−1 cm−2) and large excess of air (93.75 Ncm3 min−1 cm−2). These conditions are typical of stacks, where high H2 utilization is targeted, but are uncommon in single cell testing. H2-based mixtures were supplied between 550 °C and 750 °C, varying the partial pressure of H2 (between 93% and 21% with 7% H2O mol/mol) and H2O (between 10% and 50% H2O with 50% H2). I/V and EIS measurements were collected and analyzed with a 1D+1D model of a SOFC with rectangular duct interconnectors. At 750 °C and 93% H2, 58% fuel utilization was obtained, which raised to 81% at 21% H2, driving the SOFC under internal diffusion control. The model analysis confirmed that nearly-isothermal conditions were retained thanks to efficient heat dissipation, and that air acted as a coolant. During testing, the contact resistance grew to 0.16 Ω cm2 at 750 °C, limiting the SOFC’s performance to a maximum power density of 340 W cm−2 with 7% humidified H2. The kinetic parameters of the anodic reaction were derived by fitting, finding a positive order for H2 (+0.9), and a negative order for H2O (−0.58).