Well, we have cauldrons. We have also some vegetables (like carrots and onions). So, here's the idea: make soup using a cauldron. Since it is mainly water, it shouldn't give FEPs. It should simply replenish the hunger bar, similiar to the tea with stamina. Of course, a bowl should be needed. You could replenish the bowl by right-clicking on the cauldron (well, there should be an option to empty the cauldron too). Since it is a liquid, you could also take away using a waterflask or a similiar item. Maybe after some hours it could change into cold soup and so reducing its effects.
It should be noted that a noticeable amount of vegetables should be needed. At least 2 onions and 2 carrots for liter of water.