Burinmg oil for no reason and no leak

First look at PCV, a bad PCV can cause excessive pressure in the crankcase and pushes the oil out the engine's seals and gaskets. If that looks ok, try a leak-down test, maybe you have a broken piston ring or excessive blow-by.

1 quart in 2,400 miles is not that bad for modern thin oil. Welcome to the future.

He's right but the oil control rings could be sticking as well as the oil return holes behind them could have become restricted not allowing most of the oil to return to the crankcase. Have a friend follow you onto the highway, open it up then let off the gas, a small puff off smoke when you let off would indicate that in which case i would recommend to have a reputable european shop flush the oil system with specific cleaners