Valve stem seals. Been there done that. And my oil consumption was through the roof. 1qt/400Km (1qt/250miles).
And it's not "normal" to for these engines to burn oil. After I tackled the issue, no more smoke, no more burnt oil. Haven't added a drop in almost 7 k miles, which reminds me I have to do an oil change.

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Stable: e92is, e46 M54B25, e83 N52, e53 N62 - sold, e39 M54B30 R.I.P.