Smoke coming from the driver side vent

Hi,

I have the car listed above, right side steering wheel.
the car is in good condition, however, I was travelling for a week and didn't drive the car (car was parked in my garage). When I got back from travel and drove the car for 3-5 minutes, a white smoke with burnt oil smell came out from the driver side vent. I pulled over and turned off the engine, then more white smoke with more smell came out and stopped after 20 seconds. I parked the car in garage and did not drive for another week. When I started the engine after another week the same smoke with the same smell came out from the same place after 30 seconds from starting the engine.

similar thing with smaller amount of smoke had happened about 2 months ago when I didn't drive the car for a few days, but after driving it several times I hadn't seen this smoke.

In addition to this, I have seen some white substances on the floor under the car under where dashboard or engine is located. I noticed that when it rains the drops under this area form a thin white layer on the floor when it dries. I attached some photos.

I took it to a mechanic first time this happened 2 months ago and he changed the oil caps on the back side of the engine but it has not worked.

I highly appreciate any idea what could be the reason and solution for this?