How would you go about creating an inside out gradient to this irregular shape?

I've been having a hard time creating a gradient that acts like a radial gradient (going inside out) but instead of the gradient having a radial shape, the gradient shape mirrors/respect the edges of whatever shape it applies itself to. (In this case, this curly brace shape. I want the inside to be white, progressively becoming black as it approaches the edges, just like with the circle above it)

I've been trying with the blend tool, but I was wondering if there was a better/more efficient way to do this as even with it it I'm struggling to make it respect the edges correctly.

Thank you for your help.