As Protoss, how can I counter mass Battlecruisers in PvT?

I would say Void Rays, they can focus on each BC and deal huge damage over time. They are made for this type of situations, if stacked correctly they should win again BC's. Even better if they are backed up by Hight Templars with Psy Storm, they can be transformed into Archons later. Even batter if you can add a Mothership.

BC vs Void Rays

Early game, go for stalkers. Keep them around your mineral lines and protect your probes. It's true, you cannot do much at this stage if the BCs just teleport away but your priority should be to gather resources to build up the counter army. Build shield batteries to assist your stalkers.

After the 10 min. mark replace those stalkers with Archons.

Once you've got three bases, go for Mass tempests. Use revelation to scout ahead and hallucinations to increase the survivability of your tempests. Your tempests will undoubtedly outrange his BCs and winning should be fairly easy with this deathball if your macro is good enough.