I think I have figured it out, in great part thanks to the helpful posts here.

First thing I did, I bought myself a brush from about 1900. I think it's horsehair, quite stiff compared to the cheek-pampering super-badger to which I'm accustomed.

Anyway, this is how I use this awesome 2-piece mug now.

Step 1: I take it apart, warm it up under the hot-water faucet and fill the bottom half with steaming-hot water. I then insert the brush for a good soaking, while I do my face-prep.

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Step 2: in the top half (still detached, and still warm from the hot water), I put a couple teaspoons of Vaseline and the necessary amount of shaving cream.

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Step 3: I remove the brush, refill the bottom half with new steaming-hot water, replace the top half and, after dripping the excess water from the brush, I start whisking up an awesome lather.

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Notes:

1 - Since the diameter of the brush is only a touch over one inch, it fits the bowl beautifully and I can whisk vigorously for a good, thick, slick lather.

2 - After I lather up my face for my first pass, I rest the brush on the rim's prongs, with the bristles in the bowl, which keeps both the lather and the brush warm for my subsequent passes.

3 - The stiffer horsehair brush does a good job lifting my beard prior to shaving, and this plus its ability to retain lather with its longer bristles compensates for the slightly rougher feel on my skin.

4 - Although I still don't know whether this was the way in which this mug would have been used historically, I am getting some pretty awesome shaves out of it!

Happy shaving!

Corgi