What do I need to read, in what order, in order to make a simple shader that does this?

Basically, I have a big Plane, and I want the user to see a little piece of it at a time using another smaller Plane.

Is this a problem I would use a shader to solve? If so, how?

Yes. Read about Stencil.
An example from Alan for built-in render pipeline:
https://www.alanzucconi.com/2015/12/09/3873/
And through URP RF from Cyanilux
https://twitter.com/Cyanilux/status/1193513267534151680

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