Can this question be answered in terms of the relationship between handedness and hemispheric asymmetry. so the left hand controlled by the right hemisphere, and right hand controlled by left hemisphere.
"Are the two halves of the brain mirror images of each other"
I'm not sure if this will answer your question but here goes.
If we look at the two hemispheres say from a axial view (looking down from the top), we'd find there's some asymmetry there. In terms of internal brain structures and "regions" yes, what's in the left hemisphere is also in the right hemisphere.
If we then look at function or "activity" related to certain actions and or cognitive processes in a "neural typical"(brain of a "normal" person) you'd again see some asymmetries. For example, spoken and written language is USUALLY , primarily "processed" by the left hemisphere.
There's a contralateral nature in terms of wiring for the left and right portions of our brains and body & this may just be a consequence of wiring. However, if say you take a patient who's missing some portion of their brain, in the left hemisphere, where there is an association of some function to activity in that brain area and if this is the condition from a very early age, what you find is the right hemisphere for that area will take over that function.
If they have the same structures, same sulci and gyri, and can take over the function of the other half(to an extent) when the other half is damaged does this mean they are mirror images? I don't know.
In short, it's difficult to give a definitive answer for this (at least with my limited knowledge).