I have a small brewery in my basement that currently plugs into an outlet (I don't know the name of) on a 60 Amp 240 vac GFCI breaker, wire is 6 AWG. I want to upgrade my system with one that has two L6-30 plugs, not the same as I have now. Is this as simple as taking out the old outlet and replacing it with two of the new outlets or do the new outlets need to be on separate 30 amp breakers? I only have 1 empty spot in my panel. When I searched for an answer to this I found something similar involving wall ovens but seemed specific to them.
Depending a great deal on EXACTLY what you have now and how it's wired:
Possibly you could replace your current 60A outlet with a sub-panel and put two 30A breakers in the sub-panel for your two 30A outlets. That will only be the case if what you have now has 4 separate wires feeding it (Hot, Hot, Neutral, Ground - also known as L1, L2, N, G) or 3 wires plus a continuous metallic conduit which acts as ground.
If this is an old installation without a separate grounding conductor, you can replace the cable you have now with a cable with 4 wires, 4 wires in plastic conduit, or 3 wires in metal conduit (the metal conduit acts as ground) and still place a sub-panel. In that case you might want to consider using a larger size of wire and a larger breaker to feed it, to allow for future expansion, if your service / main box will support that.