The brief
The X1 had been leaving oil spots where it parked, the oil level kept dropping, there was a burning smell after drives, and the engine had got a touch rough at idle with a low-oil warning. He brought it in. Those symptoms point at the oil filter housing. On these BMWs the oil filter sits in a housing bolted to the side of the block, sealed to it with a gasket and often feeding the oil cooler too. Over years of heat that gasket hardens and stops sealing, so engine oil weeps out, which is the spots, the dropping level and the burning smell when it drips onto something hot. Let it run low and the engine starts complaining, which is the rough idle and the warning. A common failure point on these, and one you fix before the level gets away from you.
The diagnosis
On the lift the leak traced cleanly to the oil filter housing gasket, weeping along the seam where it bolts to the block, with the valve cover and the other seals dry. The gasket had hardened past sealing, exactly the known failure on these. That's a gasket replacement, drop the housing and reseal it. The bolt seats and the housing itself were fine, so it was a fresh gasket, not a new housing.
The work
The oil filter housing was unbolted, the old gasket removed, and both mating faces cleaned back to bare metal. A new genuine BMW-spec gasket went on, the housing torqued back up to spec in the proper pattern, the oil that had tracked down cleaned off, and the engine topped back to the correct level with the right spec oil. Then it was held at idle and checked underneath to confirm the new seal was dry. A road test followed to confirm it stayed dry and the level held.
The outcome
Dry housing, no spots under the car, the oil level holding, no burning smell, and a smooth idle with no warning lights. The X1 went home with the leak closed off. An oil filter housing gasket leak only spreads, and once it's letting the level drop the engine pays for it, so resealing it on the first signs kept it to a tidy job.