Your house appears to be double-wythe brick construction, where you have two layers of brick, and 90 degree tie bricks about every six courses to tie the two brick layers together. That means the underlying brick wall should be quite sturdy.

How much work was it to chip off the area of stone you showed in the picture? If you did that by hand, then using an air chisel with masonry bit would be way faster.

If you could chisel off the rock until you get a reasonably smooth surface, then you can decide what else would work for wall covering. The best choice would be a framed wall with insulation and drywall, but it looks like you may not have have the space to frame an inner wall. However, you could try using 2x2's or 2x3's to make it a little thinner, and spray foam the cavity for insulation and vapor barrier. Even thin furring strips are an option if you don't care about insulation.

The other choice would be to chisel off the rock and then skim coat the wall with a light coat of masonry finish. It would not provide any insulation, and not much of a vapor barrier, but a good installer can make it very smooth. Its relatively common to coat an interior brick or block wall with that type of finish in basements.

Bruce

Rotary hammer on hammer only with tile removal bit would make quick work of it. Board up the window and door first. Stones will be a-flyin'. Wear a full face shield.

Would need a stucco job following that, it will look a mess after stone removal.

How about leave what you have and skim coat a finish on top of the rocks? Maybe leave a few rocks (not sharp ones) exposed to make the wall more interesting.

I think that this problem would best be solved by a realtor.

Honestly, I think I'd look at attaching furring strips and drywall. Skimming that with concrete / plaster would be the next option but would be a bear.