What a Rump Steak is depends on where you are. North Americans have a completely different interpretation from the rest of the English-speaking world, and in France, it's completely different again, taken to higher levels of refinement.
When you are looking at recipes for Rump Steak, it's very important to suss out what audience the recipe is primarily addressed to. You can't cook a North American Rump Steak the way you would a British or New Zealand one, as they are actually two very different cuts despite the name being confusingly the same.
North American Rump SteakIn North America, a Rump Steak starts off as a larger cut known as a Rump Roast of Beef, from the Round area of a cow -- it's hindmost area. This cut is boneless. (See main entry for "Beef Round.") It will have next to no marbling or fat. This larger cut is then cut into smaller portions known as steaks.
You may sometimes see it labelled as a "Butt Steak", or as a generic "Round Steak."
It really does need slow, moist cooking such as braising, though with pounding and / or marinating you can transform it into something that can be pan-fried.
British Rump SteakNorth Americans getting British-based advice about cooking a Rump Steak will be confused when they see people treating it as a grilling steak. That's because it's a completely different cut of beef. In Britain, Australia and New Zealand, a Rump Steak is cut from the area they call rump of a cow, which takes in the areas North American butchers call "Sirloin", "Tenderloin", "Top Sirloin", and "Bottom Sirloin", with none of the round at all. It will have good marbling. Though it's a cheaper cut than sirloin steaks, many chefs will still use it in their restaurants as they consider it to have superior flavour.
Here are some quotes reflecting the attitude of British foodies towards what are known as Rump Steaks in the UK:
"Rump is the other extreme. It's always moving backwards and forwards so there is a lot of muscle in there. The fat is in the meat so you have marbling. Rump always has the best flavour." - Tim Wilson, The Ginger Pig butchers in Levisham, North Yorkshire. 2008. Quoted in 
"I really love a thick piece of rump cut from a piece of beef that has been hung on the bone to mature for 21 days. Pan-fry it very quickly in a really hot pan to seal in the juices, then finish it off in the oven for about five to 10 minutes until it is medium-rare -– fantastic stuff! A really classy piece of rump has all the right ratios of fat, muscle structure, fibre and flavour." - John Torode, Smiths Restaurant, Smithfield Market, London. 2008. Quoted in 
French Rump SteakIn France there are three possible Rump Steaks, starting with one specifically cut as a steak.
Coeur de romsteckIn France, butchers start with a centre cut from the rump that they call the "coeur de romsteck", meaning "heart of the round" steak. This can be used as a steak on its own, or further refined.
Filet de romsteckThe next step of refinement in a French Rump Steak is a "filet de romsteck" -- "filet of round steak". To make this cut, butchers take a "coeur de romsteck", and trim away all the fat and ligaments. What is left after that trimming is the "filet de romsteck."
A "filet de romsteck" will end up being a cylinder of meat about a foot (30 cm) long that looks something like a tenderloin roast.
Pavé de romsteckThe third and final cut that can be made is called a "pavé de romsteck" -- sort of meaning a "paving stone of round steak", a "squat slab." It is a the long "filet de romsteck" cut into individual serving-sized portions.
 Morris, Sophie. "Fillet or sirloin, rump or ribeye, getting your beef in tip-top shape requires good ingredients, skill and a little alchemy." London: The Independent. 25 September 2008.
Beef RumpBeef Rump; Rump Pot Roast; Rump Steak
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