Maybe something resembling the cementation process to make blister (or shear) steel.
The wikipedia page describes a process of alternating wrought-iron bars with charcoal in tall stone containers that were then sealed on top with a refractory mixture of powdered charcoal, soot and mineral salts. The stone container was then heated from below, the process taking a week or more depending on the amount of iron.
Let's say wrought-iron is our common ore-smelted iron.
We could then have either:
A - a separate building for the cementation process
B - special containers to put into the existing ore smelter.
Into the A or B container you put iron and charcoal in different proportions.
The container has to be sealed with a mixture of powdered charcoal and coarse salt (or maybe mineral salt extracted from mines).
The fire is lit...
Now comes the fun part where the proportion of iron vs charcoal and the time you maintain the furnace lit both influence the quality of the steel produced.
More carbon could make the steel hold the edge better but be somewhat brittle... (or, in the absence of durability, other drawbacks...)
Less carbon would increase ductility and flexibility, maybe a better solution for construction uses?
Before you can use blister steel though you must first hammer it multiple times because it has absorbed carbon in its surface only (the iron doesn't melt in the process). In a process similar to the folding and hammering used to make katana blades hammering multiple times improves the result.
This last process would be very time and phlegm consuming.
In alternative you could melt again blister steel into a crucible to make crucible steel.
To make the steel production more unique as a mechanic, a system could be devised where the various minor components in the steel alloy would interact with one another, giving to the final product bonuses similar to those achieved in slotting. This way you would have tailors slotting clothes and blacksmiths making a range of steel alloys for various purposes.