Step 1: Build a template library
Well, this part might be a tad morally controversial, since it basically involves taking a few hundred soldiers and ... uh... slicing them up into really thin, 10nm wide slices. Obviously this presents interesting technical challenges, including non-destructive tissue vitrification (forgot to mention, you gotta turn your soldiers to glass first), nanometer resolution scanning and feature resolution across the slices. Basically you have to figure out how to freeze a human into a glassy substrate mid-breath and then scan them and reassemble the giant 3-D jigsaw puzzle into a meaningful whole again. This is, needless to say, many orders of magnitude beyond our current computational and matter-control capabilities, but nothing (besides maybe the near-instant non-destructive vitrification bit) is physically impossible.
Once these few near-impossible steps have been achieved, you have your template library. At first you'll want to rebuild exact clones, but as the cost per build decreases (practical, hands-on experience with doing stuff almost always brings the per unit cost down), your engineers can start playing around with chimeras, combining the best features extracted from across specimens.
Step 2: Full in-silico instantiation
Build an in-silico model of the complete build. With realistic physics and some significant supercomputing muscle, a "build" could be tested in virtual reality for seconds (or if the funding is particularly generous maybe even weeks or months) before it is judged fit for a fleshbuild.
This is particularly used for testing blended builds, or daring tweaks to an existing model. Particular parameters can be altered (let's up aggro to 17/25, and test if it can still obey orders, or just going on bloody indiscriminate rampages). Depending on the battlefield purpose, certain features that would prove lethal in days or socially undesirable in human soldiers that would have to function in a society could be baked into the vatgrown. Think replacing the digestive system with a glycogen store, if the specimen has an expected lifetime measured in days.
Step 3: Good old-fashioned 3D printing
Again, depending on the per-unit cost and the expected durability, certain shortcuts and digital workarounds can be made. If the per unit cost is in the tens of millions of dollars and durability in years, you can build many redundant systems (2 hearts, advanced stop-bleed tech, etc), whereas if the cost can be brought down to roughly the current price to produce a calf in the West (about $1000) and the expected life-time is in days or hours, you can skip many life-maintenance systems that would be needed in a longer-lived or more valuable specimen (I already mentioned replacing the digestive system with an energy storage as a possible example).
The most complex parts will probably be the wiring diagrams of the brains. Human neurons usually take years or even decades to wire themselves into a useful network, with slow dendritic and axonic growth and pruning of synaptic connections. Presumably, with proper chemical prodding the neurons can be coaxed into linking much faster and along predetermined paths. The amount of information stored in this will be truly enormous. The human wiring diagram relies on a few tens of megabytes stored in DNA (nowhere near enough to specify the cross-wiring of billions of neurons), and makes up the rest with chaotic growth followed by aggressive pruning. Presumably, your builders can rely on a version of this on metaphorical steroids. Explosive dendritic growth followed by ruthless pruning. Nanomachinery, directed microwave activity, lasers ... there are many options here. Alternatively, you can skip the whole wetbrain and go for bionic options, with in-silico (computer)-ran versions, which may often be faster and more capable than the biological versions.