What is the recommended spark plug gap setting for 2005 Mini cooper S and should it be the same for Iridium plugs

The ideal gap will probably not be the one quoted in the Mini data.
You should refer to the spark plug manufacturer's catalogue which will provide the information you need.

If they are Iridium spark plugs, they come with pre-set gaps. Don't re-gap them.

Otherwise if using another spark plug make your gap should be 0.44

it should be .045". depending on the year there maybe a sticker/decal under the hood that says what the plug gap is.

The spark plug gap? If you are using platinum or iridium plugs (recommended), do not measure the gap as you will damage the plug.

Due to the fact that these are iridium plugs, resetting the gap is not recommended as it typically damages the plug. However, the specified gap is 0.060 inches per the Autozone online repair guides.

The OEM plug for your vehicle (NGK BKR6E-N-11) comes pre-gapped from the manufacturer at .043" (1.1mm).

I prefer bosch plugs :

2000 Chevrolet Tahoe 5.3L 323CID V8 GAS FI T - GAP=0.040"; Original equipment is iridium. 2000 Chevrolet Tahoe 4.8L 294CID V8 GAS FI V - GAP=0.040"; Original equipment is iridium. 2001 Chevrolet Tahoe 5.3L 323CID V8 GAS FI T - GAP=0.040"; Original equipment is iridium. 2001 Chevrolet Tahoe 4.8L 294CID V8 GAS FI V - GAP=0.040"; Original equipment is iridium. 2002 Chevrolet Tahoe 5.3L 323CID V8 FLEX FI Z - GAP=0.040"; Original equipment is iridium. 2002 Chevrolet Tahoe 5.3L 323CID V8 GAS FI T - GAP=0.040"; Original equipment is iridium. 2002 Chevrolet Tahoe 4.8L 294CID V8 GAS FI V - GAP=0.040"; Original equipment is iridium. 2003 Chevrolet Tahoe 5.3L 323CID V8 FLEX FI Z - GAP=0.040"; Original equipment is iridium. 2003 Chevrolet Tahoe 5.3L 323CID V8 GAS FI T - GAP=0.040"; Original equipment is iridium. 2003 Chevrolet Tahoe 4.8L 294CID V8 GAS FI V - GAP=0.040"; Original equipment is iridium. 2004 Chevrolet Tahoe 5.3L 323CID V8 FLEX FI Z - GAP=0.040"; Original equipment is iridium. 2004 Chevrolet Tahoe 5.3L 323CID V8 GAS FI T - GAP=0.040"; Original equipment is iridium. 2004 Chevrolet Tahoe 4.8L 294CID V8 GAS FI V - GAP=0.040"; Original equipment is iridium. 2005 Chevrolet Tahoe LS 5.3L 323CID V8 FLEX FI Z - GAP=0.040"; Original equipment is iridium. 2005 Chevrolet Tahoe LS 5.3L 323CID V8 GAS FI T - GAP=0.040"; Original equipment is iridium. 2005 Chevrolet Tahoe LS 4.8L 294CID V8 GAS FI V - GAP=0.040"; Original equipment is iridium. 2005 Chevrolet Tahoe LT 5.3L 323CID V8 FLEX FI Z - GAP=0.040"; Original equipment is iridium. 2005 Chevrolet Tahoe LT 5.3L 323CID V8 GAS FI T - GAP=0.040"; Original equipment is iridium. 2005 Chevrolet Tahoe Z71 5.3L 323CID V8 FLEX FI Z - GAP=0.040"; Original equipment is iridium. 2005 Chevrolet Tahoe Z71 5.3L 323CID V8 GAS FI T - GAP=0.040"; Original equipment is iridium. 2006 Chevrolet Tahoe 5.3L 5328CC 325CID V8 FLEX FI Z L59 - GAP=0.040"; Original equipment is iridium. 2006 Chevrolet Tahoe 5.3L 325CID V8 GAS FI T - GAP=0.040"; Original equipment is iridium. 2006 Chevrolet Tahoe 4.8L 294CID V8 GAS FI V - GAP=0.040"; Original equipment is iridium. 2006 Chevrolet Tahoe LS 5.3L 5328CC 325CID V8 FLEX FI Z L59 - GAP=0.040"; Original equipment is iridium. 2006 Chevrolet Tahoe LS 5.3L 325CID V8 GAS FI T - GAP=0.040"; Original equipment is iridium. 2006 Chevrolet Tahoe LS 4.8L 294CID V8 GAS FI V - GAP=0.040"; Original equipment is iridium. 2006 Chevrolet Tahoe LT 5.3L 5328CC 325CID V8 FLEX FI Z L59 - GAP=0.040"; Original equipment is iridium. 2006 Chevrolet Tahoe LT 5.3L 325CID V8 GAS FI T - GAP=0.040"; Original equipment is iridium. 2006 Chevrolet Tahoe Z71 5.3L 5328CC 325CID V8 FLEX FI Z L59 - GAP=0.040"; Original equipment is iridium. 2006 Chevrolet Tahoe Z71 5.3L 325CID V8 GAS FI T - GAP=0.040"; Original equipment is iridium. 2007 Chevrolet Tahoe LS 4.8L 294CID V8 GAS FI C - GAP=0.040"; Original equipment is iridium. 2007 Chevrolet Tahoe LS 5.3L 5328CC 325CID V8 GAS FI J LY5 - GAP=0.040"; Original equipment is iridium. 2007 Chevrolet Tahoe LT 5.3L 5328CC 325CID V8 GAS FI J LY5 - GAP=0.040"; Original equipment is iridium. 2007 Chevrolet Tahoe LTZ 5.3L 5328CC 325CID V8 GAS FI J LY5 - GAP=0.040"; Original equipment is iridium

Hello there:
The recommended spark plug gap for a 2003-2004 Honda Odyssey is .044"
Keep in mind, many OE manufacturers (i.e. Denso, NGK) pre-gap their plugs for specific applications. If you happen to buy the iridium or platinum style plugs with the very thin center electrode, they should come pre-gapped. It can't hurt to check the gap before installing the plugs, but if any adjustment is necessary, do so with caution because the ultra-thin electrode may crack if any excessive pressure is placed on it.
Hope this is very helpful
Best regards Michael