Is it possible to synthesize a nutritional food source completely from inorganic materials?

I have a work-in-progress scenario where an interstellar generation/ark/cryogenic ship has reached its destination, but there are no habitable planets. There's no turning back, and so now the colonists have to try and eke out a living in space and/or airless planetoids. At least initially, there is no suitable habitat to have farms, and not sustainable for the given population.

Given there is plenty of energy available, a small amount of existing organic material to be recycled, and carbon, hydrogen, nitrogen, oxygen, phosphorus, sulfur and possibly other chemicals available to be gathered/extracted/mined, is it technically/realistically feasible to be able synthesise a constant life-sustaining completely nutritional (if not appetising) food/substance? I'm looking for something more Haber process rather than Star Trek replicator.

The precise details of how this would work aren't too important; I just want to avoid a possible plot hole.

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Is it possible to synthesize a nutritional food source completely from inorganic materials?

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