From time to time, while parking, my engine 'chuckles', almost turns off.
No problem was found by the dealership.
I had one coil replaced a year ago.
Any idea?

 

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So you are parked and the car is running at idle for 10-15 min? Does the RPM fluctuate randomly from time to time and than the car dies? Classic HPFP symptoms. This pump used to be $399.00 USD 2 years ago and now is over $1200 USD at many dealers here.
The other parts are suspect, but the above is very classic to what happens. This and also a 2-3 attempts to start the car when cold.
Let us know what you find out. Both the low pressure in tank pump and the engine mounted High pressure pump can be measured outputs with the lap top and scan tool.