You have low fuel pressure in the morning, resulting in a hard start, or start stall. once the pressure rises, it runs great.

On a hot restart, your leaky injectors are causing the engine to flood, which will cause it to rumble on restart, once it burns out the excess fuel, it runs fine..

Your symptoms might not be as severe, but I think the shoe fits.

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Eugene

10 E63 AMG
93 300te 4matic
07 BMW X3
14 Ford F-150 Fx2