Use normal drywall finishing techniques and then add the crown molding to match the existing molding.

Some might suggest a medallion or decorative overlay in the center of the box. But it would pose cleaning problems. Would not want it in my house.

How about tile? It could be ceramic or metal.

Buy the stainless chimney extension to replace the drywall. Or have one made.

I am with the idea to Finish the dry wall and moulding.

To add a little flare. The top section between the stainless and the ceiling would be a good place to put a small self unit running the full width with two or three shelves 3 to 4" wide. Add a few old small bottles, jars or other knick÷knacks.

Or grab an old fashioned metal sign to hang there.. Thousands of different originals and reproductions can be gotten in about all shapes and sizes.

Wrap the drywall in Chemetal:

Here is a link that might be useful: Chemetal