In the basement, we got done getting drywall up, but there is a gap between the frame and the brick wall. In addition, Perma-seal put there cover up the wall. Eventually, the window will completely replaced and a frame will be installed. For now, I would like to fill the gap between the brick wall and the wood frame. Insulation was installed, however I don't want to fill it with that as I have a cat who likes to look out the window and don't want that getting on her. What can I easily put in there that's not too costly? Appearance is not a large concern.
What about just drywalling the faces of the 2x4s and letting it hang off, to fill that 2.5" gap? E.g., use a 6" wide strip. You should probably plywood the bottom sill for safety (yours and the cat's) before you drywall it.
Use corner bead and mud it for a 'temporary-permanent' solution, after you do shove a little more insulation back there.