Big puff of white smoke at start up after sitting for several hours.

Black smoke is too much fuel. My guess would be that there is an injector that is stuck open draining the pressurized fuel into a cylinder or several cylinders. And that is a considerable amount of fuel. And it would account for the hard start because there isn't any fuel being pumped into the other injectors until the pump builds the pressure back up.

It sounds like it has jumped time. What year is the car and how many miles. Timing chains can go bad as early as 70,000 miles

Could be a coolant leak into the cylinder. (head gasket leak) use a five gas scanner to check for hydrocarbons in cooling system.

Regarding 2001 audi a6 quattro 2.7t....i was driving to work the car was fine then white smoke starting coming from under the hood and tail pipe. i stopped veilce and alot of oil was dripping from front of car. I towed it home and i looked under the hood and there was oil from valve cover gasket. i let the car sit for a few days, had it running again for a good hour and no white smoke was coming out. I removed the valve cover and gaskets are all bad. i want to know can the valve cover gasket leak cause the white smoke to come from exhaust pipe?

Sounds like the valve guides are leaking oil into the cylinders, or there is a coolant leak somewhere. Usually white smoke is coolant but could be oil.
Are you adding either fluid often ?

Check the fuel system pressure--if low, a weak fuel pump may take some amount of time to restore sufficient pressure to start. Does the exhaust emit black smoke for a short time when having starting trouble? This could point to leaking fuel injector(s). Don't know whether doing a computer scan would show anything, but maybe worthwhile. Go to Autozone or similar business for a free scan. Hope this helps!

What color is the smoke? White smoke is moisture/steam - which can indicate coolant is leaking into the engine (head gasket going bad).
Have you noticed your coolant level going down? Check the level in the overflow tank and the radiator each day (after the car has sat for several hours) and see if it slowly goes down.

Don't rebuild that engine. Replace the head gasket. machining the head is not necessary. Clean both surfaces with fine emery cloth.

What engine? 5.7? If yes, replace the distributor cap.

I had a similar problem with my 2003 325iT w/59K miles last week, right after an oil change. It did it more often when starting the car, and once or twice when accelerating. Then it stopped smoking and hasn't in several days. My mechanic neighbor suggested that it may have been too much oil, that has corrected itself by burning off. I hope he's right. I figure the smoke stopping is either a good thing or a really bad thing. No engine warning lights or anything, so I guess all is well.