As long as the moon is spherical in shape, it'll cast a circular shadow. The two suns would only make the "iris" irregular, unless all three bodies were in conjunction(all in one line), when it'll look just like our eclipses.
For an elongated pupil you need a satellite that is not in hydrostatic equilibrium, which means that it is less than 500-600 km across.
It's shape could conceivably resemble a tri-axial ellipsoid(
http://en.wikipedia.org/wiki/Ellipsoid).
It'll have to be in a closer orbit than the Moon is, to obscure enough of the solar disc to for a meaningful eclipse.
Due to the small size and close orbit, it'd most likely be tidally locked with the parent planet(unless captured very recently), with the longest axis facing towards it, and presenting the flattened ellipse to any observer.
Assuming a single star in the system(you don't really need two) of the same apparent size as the Sun, the moon's orbit would need to be around 100 - 150 thousand kilometres(~3 times closer than the Moon) to obscure the disc from edge to edge. Note that such a shape of the shadow would only be visible from a relatively narrow band of the surface of the planet, just as it is with total eclipses on Earth. The rest of the planet would see a partial eclipse at best, with the point of the "cat's pupil" grazing the solar disc from one side or the other(depending on lattitude).
Anyway, shorter orbit means shorter orbital period(Kepler's Third Law), in our case around 1/5th of the lunar month, i.e., 5-6 days.
You could either make this a very common occurrence by keeping the orbit of the satellite in the same plane as the ecliptic, or a rare one by increasing the inclination(so it's e.g. once or twice per year, or rarer, but not more frequent - compare with eclipses we've got on Earth to get a feel for how it'd look like).
You could also use the binary system to add rarity value to the eclipse, as unless the satellite's orbit lies in the same plane as the plane of the binaries rotation around their common centre of mass, the eclipse would happen only when it coincides with the two stars being in conjuction. Otherwise the moon would keep passing between the two stars.
And if it were in the same plane, then it'd obscure each of the stars every 5-6 days one after the other, and both at once during the conjunction, which in turn would probably happen every few weeks to few months, depending on the specifics of the binary system(can't be too long a time, as it'd make the planet unlikely to maintain a stable orbit in the habitable zone).
This kind of eclipse could be made arbitrarily rare, I think, as you can choose the period of rotation for the binaries in such a way that the satellite's passage rarely coincides with conjunctions.