If your space-travelling-species didn't start this way it should be possible to create a scenario in which they rely solely on one food-species.
The problem with only one type is: it normally does not contain enough nutritions. You will rarely find everything you need in one type of food, especially if your space-travelling-species is supposed to be a highly difficult organism, which it probably is, if they want to go to space.
But: there are quite a lot of animals on our good old earth, that have (nearly) only one source of food. Therefore your species could quite easily start with one primary food-source that makes up most of their diet.
When they evolved they realised, that their primary food-source is far better for them than any other food they could find:
- the food-species was very fertile
- they were very resistant to environmental problems and changes
- there weren't many other predators trying to hunt the food-species
- they are very nutritious, so that your space-travelling-species only needs small amounts of other food
- they didn't take up much space compared with other foods
- it was easy to keep them confined and fatten them
- they contained lots of useful things: a lot of meat to eat, bones to make tools, etc.
- easy to guard from other predators
Because of these reasons they started breeding the food-species more and more. They made them fatter, more resistant, etc. Everything we did with animals like chicken, pig, cow, etc.
You have a space-travelling-species, so their technological level should be beyond ours, so at some point they started bio-engineering. They added whatever they needed to the food-species and started breeding them more than ever before. Soon your species had an animal that could give them everything they needed. They relied only on this one kind of animal. And because their organism was already adapted to this source of food the following generations started to be unable to use other sources of food.
And this was the point, when your species changed from one, that was relying heavily on one type of food to one that relied solely and exclusively on one type of food.
After this they needed to spend some time on details, like how to best store the food. But I imagine if your species has always heavily relied on this one source of food they have evolved very refined methods of keeping their food intact and transport it in the most efficient way possible.