The pan would look something like this:

To cook it, you'd need to put it in your oven like this:

(This is all patent pending, of course.)
One problem with this method is that the brownies cooked in this pan do not have a top, they just have two bottoms where the brownie was baked in contact with the outer or inner edge. One way to get around this would be to cook the brownies about half-way, then open the oven and take out the inner sphere. The hope would be that the brownie mix would stick to the outer sphere and the inner brownie edge would form the top. But then one has to wonder why the brownie mix would be sticking to the outer sphere the way we want but not sticking to the inner sphere when we tried to remove it.
A second, more compelling problem is that the brownie mix actually expands (slightly) as it cooks. If the brownie pan was filled up all the way and closed tightly, it might explode as it cooks. This minor kink may need to be worked out. I'll let you know how the trials go.