How do I cover up this partially exposed brick?
I would not even mess with that. Trying to apply some substance to the brick will be a very tricky operation.

The best option is probably to build a drywall box closely around it. Doing that guarantees that everything will be flat and easy.

Two notes:

(1) Make sure the boundary areas at the top and bottom are absolutely sealed off, not even a pencil should slip through. Otherwise such spaces can be used by rodents and other vermin to travel around inside the walls of the house.

(2) If any cords or wire would be run at any point in the future through there, install thinwall EMT as necessary and attach it to the brick so it cannot move.