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I have a thermometer like this:
Today I'm making tostadas. I don't need or want deep oil for that, just over a centimeter would be plenty. In order to submerge the bulb of this thermometer in oil that shallow, the bulb would almost be touching the bottom of the pan. Would I get even close to an accurate reading that way? Is there an accepted minimum depth for using a thermometer of this type?
That is probably not deep enough to get an accurate reading. It varies with the thermometer, but usually you need at least a couple of centimetres to be submerged to get an accurate reading. Also, unless you are super careful, it will be nearly impossible to stop the thermometer touching the bottom of the pan. In my experience the clips on these doohickies are terrible for adjusting the angle of the thermometer.
When shallow frying in this manner I usually just go by rules of thumb. One that has never let me down is to use a wooden chopstick. When you think the oil is getting hot enough, place the tip of the chopstick in the oil. If bubbles rapidly appear around the chopstick, you're hot to trot.
There are certain details missing here that would make this problem easier to solve. I would want to know what kind of pan you're using, what kind of oil you're using, and what temperature you're shooting for. However, even without knowing these things in an other than general way, there is still an approach you can use which will meet your stated aims.
Using whatever oil you intend, add to your pan significantly more than you know you'll need. Perhaps half an inch or more. Crank up your heat to something reasonable. Give the oil a chance to really heat up. Check it with your thermometer. Holding it in a well gloved hand is fine. If it falls below your target temperature, (meaning hasn't reached it yet), wait awhile longer to see if more time is needed. Next time you'll be able to tell whether to crank the heat up a bit more. If, however, the oil has already exceeded your target temperature, obviously you'll have to turn it down a bit and work this same process in reverse.
Sooner or later you'll be able to tweak this amount of oil to your target temperature. The beauty here is that the setting you've found will work just the same on the lesser amount of oil, that is, so long as you keep all other things equal (same pan, same kind of oil). In other words, whatever temperature your larger amount of oil gets to (unless it's excessively large) is the same as what your smaller amount of oil is going to get to (unless it's excessively small). So once you've got everything determined, you won't need to make any more temperature measurements. This wouldn't be true for the skinniest amount of oil. But it's fine for what you describe.
So, without in any way adjusting your heat settings, just pour off all of the extra hot oil and return your pan to the burner. Because you've fine-tuned your settings your oil will rise to your target temperature and not exceed it. Just wait a bit each time you find it necessary to add a little oil (the tostadas will absorb a bit themselves) since, of course, the cool oil will need time to reach the target temp. For greater convenience you could perform this same process on a small pot of oil on a back burner, so that while you're frying your tostadas you'll always have instant access to oil at the proper temperature which, that is to say, you can just ladle on over into your pan. Muy buena!
