The brief
The A3 was getting through oil faster than it should, idling rough, hesitating, and the check engine light was on. He brought it in. That points at the oil separator in the crankcase breather. As the engine runs, pressure and oil mist build up inside the crankcase, and the breather system vents that back into the intake to be burned cleanly, with the oil separator catching the oil so only the gases go through. When the separator fails, oil mist gets pulled straight into the intake, which is the oil consumption, and the failed unit upsets the crankcase pressure, which leans out the idle and trips the light. A failed oil separator doesn't recover, so it needs replacing.
The diagnosis
Diagnostics confirmed it, fault codes pointing at the crankcase ventilation system and a lean mixture, and a check showed the oil separator wasn't holding pressure as it should, pulling oil through the breather. The intake, the injectors and the rest of the engine checked out. That's a replacement. The separator and its diaphragm are sealed into the breather unit, you don't rebuild it on the car, so the call was a complete unit.
The work
The old oil separator was removed and a new genuine Audi-spec unit fitted with fresh seals, the breather hoses checked over while everything was apart. Then the fault codes were cleared and the engine's fuelling adaptations reset so it could relearn against a breather system that was working. A road test confirmed a steady idle, the light staying off, and no hesitation.
The outcome
Steady idle, clean response, no warning light, and the oil consumption back to normal. The A3 went home running properly again. A failed oil separator quietly feeds the engine its own oil and keeps the idle unhappy the longer it's left, so changing it and letting the engine relearn put the running right.