minecraft-java-editionminecraft-redstone
As of 1.6.2, what is the most compact way to cook a cow/pig/chicken with a dispenser and a lava bucket?
Or what is the most compact way to send two fast pulses in order to activate the dispenser and deactivate it fast enough so that the mob is cooked but its drops aren't destroyed by the lava itself?
Updating answer with much more compact version
I hate answering my own question but I found the answer here: http://www.minecraftforum.net/viewtopic.php?f=35&t=60816 (I was searching google for a switch diagram when I found it via station selection search since it seems most people use it for minecart stations)
Here is the schematic for anyone interested in reproducing it. This particular one is great because it's only one button wide which makes it perfect for my goal. 
Here's another one that has the indicator lights on the same plane as the button but I haven't checked this one to see how it performs. 
This setup works:
One of your items is an arrow, the other is any non-dispensing item like redstone.
Arrows will fire and miss the tripwire. Items will hit it then burn up, triggering a signal. You can use the items you suggested: arrow, cobble, cobble, arrow and the desired signal will be generated (well, the inverse).
Best Answer
Invisible parts: Under each orange block is a sticky piston facing up. The left black-framed block is a furnace with 14 items in it (acting as a signal source), and the right black-framed block is the dispenser with a lava bucket.
How it works: The input signal comes from the left. The orange block and sticky piston turn the signal into a pulse (a “monostable”, or rising-edge detector) for the dispenser. The right comparator's signal indicates the decreased fullness of the dispenser (empty buckets stack more than full ones), allowing the torch to turn on, which signals the right monostable to produce a second pulse to remove the lava. If a longer burning-in-lava time is desired, lengthen the repeater delay on the right.
It would be possible to simply produce two pulses from the input by delaying the monostable signal; the advantage of this design is that it is self-correcting if the lava is in the wrong state, because the second lava-removing pulse is generated by the dispensing of the lava. However, doing it the other way does have the advantage of needing no quartz.
This design is derived from my zombie damager, which is a continuous flow system. If you want to have this machine automatically trigger when mobs arrive in it, you could add a tripwire above the lava in the same way as that mechanism does. (The main wiring here is different from there because that machine removes the lava, rather than adding it, when a mob arrives, but the tripwire can be connected to the input in the same way.)
Finally, note that chickens are tricky because they have so little health. Specifically, even with a different pulse circuit built for absolute minimum delay, chickens standing where the lava goes seem to take enough damage to die instantly, burning their items in the lava. However, if the chicken is on a slab underneath the lava (thus being slightly lower), then it sometimes survives long enough to die after the lava disappears, and its drops will sometimes survive even if it dies instantly. (Strange that that makes a difference.) Based on this result, I recommend using something other than lava for chickens.
Tested in Minecraft 1.6.2.