Should I use water from steaming to make stock or gravy?
Does it depend from what I have steamed (e.g., potatoes or vegetables)?
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It shouldn't matter if you re-use the water you used for steaming or use fresh water. I would only use it in a few situations:
The benefits of one and two are mostly negligible because the amount of flavor or starch isn't going to be that much.
Situation three is really the only reason I would reuse the water, but most of the time cooking water ends up watering the plants.
In general I would not reuse steaming water to make gravy. As devin_s said you are unlikely to get much flavor from there. Depending on what you're steaming (e.g. spinach), however, you are likely to pick up some bitterness or other off flavors.
Water used for boiling, on the other hand, can be very useful. For example, if you have boiled shrimp with aromatics, that water can be very useful as a flavor foundation for a soup or stock. Pasta water (or potato water, I suppose) could be useful as a thickener. For example, I will often add a splash of pasta water to loosen up a thick pesto.