there are such services in Russia, tell us the city so that we could find some service closer to that city, they mostly specialize in ordinary food, but i think it's possible to find gourmet food sections on some of services,
it's logical that such services should be more developed in bigger cities
anyway, tell us the city's name for better search
for payment you will have to read the conditions, or somebody could help you if it's in Russian only, i think credit card is ok in most cases.
in this case, it can be cheaper than express mail.