Low profile cabochons?

My sister is a pilot and has asked me to make a small pair of low-profile stud earrings, so that her headset doesn't catch on them.

The problem I am finding is that all the cabochons I keep seeing are all quite domed in profile? As in a sphere cut in half. I'm after something that is closer to a disc with smooth edges, maybe a slight dome in the middle.

I was wondering if:

A - This kind of stone has a specific name that I don't know, resulting in me not being able to find them
B - Anyone can point me in the right direction to a supplier that might stock things like this?

My sister is fond of purple, so it's likely to be Amethyst, Iolite, or maybe Moonstone (which I know isn't purple...!)

Thanks all.

Manchester minerals do a limited range of flat cabs here
If she likes moonstone, she might like opal - the A grade from MM are very flat. There are things like dyed paua shell, black lip pearl (lovely) and Mother of pearl that are all flat. Kernowcraft do all of them here, or ring someone like AE Ward and say you want some low profile cabs in X stone. I've found the same stone can vary in thickness from the same supplier.