The Hammond expression pedal seems to be a mystery to many players, especially those that are more used to playing on clone wheels, even though at least some of these model the original Hammond expression pedal behavior very closely. Many people seem to think that the expression pedal on a Hammond is only used to control the volume of the organ, but this is only part of its function, it also acts as a (passive, non-linear) equalizer (EQ). When the volume is low, higher frequencies are much more attenuated (reduced) than lower ones, leading to a much bass-heavy sound and less pronounced highs. The reverse is true when the expression pedal is put to full throttle (loudest volume), which results in a much brighter sound with relatively reduced bass content.
Thus, you can influence the character setting of the tone by opening or closing the expression pedal. This may lead to an undesired low volume when aiming for a more bass-heavy tone with les emphasized highs, but this can be counteracted by increasing the amplification. This may be accomplished by turning up the Leslie or other amplifier you may be using to amplify the Hammond. This may also make drive your amp into overdrive more easily, so you may need to find the right balance in the settings of the amp and the expression pedal to give you the desired tonal balance as well as a usable travel to adjust dynamics using the pedal.
Personally I like overdriving the Leslie to get a bit of growl, and this gets much easier with the Leslie on very loud, and playing the expression pedal at the low volume end, pushing the Leslie into a nice drive when increasing the volume on the expression pedal.