Sticky Headers And Full-Height Elements: A Tricky Combination

I was recently asked by a student to help with a seemingly simple problem. She’d been working on a website for a coffee shop that sports a sticky header, and she wanted the hero section right underneath that header to span the rest of the available vertical space in the viewport.
Here’s a visual demo of the desired effect for clarity.
Looks like it should be easy enough, right? I was sure (read: overconfident) that the problem would only take a couple of minutes to solve, only to fin