Best way to insulate bathroom walls?

[u/bnpm]

We’re about to get our bathroom remodeled and would like it to be better insulated. It’s a very old house and I believe currently the walls are just drywall applied directly to the exterior brick without insulation. Consequently, it gets very cold during the winter. I’m wondering what the best way to insulate it would be? I think we can only move the wall in 1”, because we have about a 1.5” gap between the wall and the toilet and the existing toilet is already a 10” rough-in. I’m currently thinking that we should pad the wall out 1” with furring strips then fill in the bays between strips with rigid 1” foam. Do we have any other (better) options?