There is only one example that I know of an eyelet from the European medieval period. This eyelet is based on parts found and published in the Museum of London: Textiles and Clothing but differs in one way. I do not use a buttonhole stitch to create my eyelets, I use a whip stitch. Just as strong and twice as fast.
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This is an image of the tools I use, showing scale.
The top tool is a stainless steel awl. Don’t know where I got it but I think it was in my grandmother’s sewing basket
The center tool is a wooden shishkabob skewer.
The bottom tool is a sewing awl sold by Clover. I prefer the rounded handle. This is my favorite eyelet tool for several reasons.
Reason 1: It allows me to really stretch the hole out without breaking the fibers of the fabric.
Reason 2: It is comfortable in my palm
Step 1. Making your hole.
Slowly twist your awl into the fabric. The twist allows the fabric to spread around the tool and alleviates tearing the warp or weft.
Slowly push your awl and widen the eyelet hole.
A good beginning. Wool is especially stretchy. I find that I use my awl several times in the course of sewing my eyelet to keep the eyelet of useful size for lacing. A lacing point or chape must fit.
I start with a waste knot a bit away from the eyelet hole.
Step 2. I make 5-6 whip stitches around the eyelet hole.
If you have a facing, you can bury your knot between facing and fabric and forget about it.s
Step 3. At this point I re-stretch the hole with my awl.
Step 4. Whipstitch closely around the hole so that no fabric shows through and so that your first 5-6 whipstitches are covered.
Step 5. A completed eyelet.
Step 6. Using my needle I run it through several stitches, making my around the eyelet, securing my end thread.
Step 7. Carry your thread to the next eyelet hole with shallow running stitches if you have no facing. If you have a facing it will be buried between your facing and your fabric.
Step 8. Back to Step 1.
Step 9. When I run out of thread, I tie off as in Step 6. I also clip my waste knot from Step
1. The first 5-6 whip stitches, now covered with the eyelet stitches secure your thread and the knot is no longer needed.
If you have buried your knot between facing and fabric, this step is not necessary.
All pretty with knot clipped.