Here we have a basic vertical stack being countered by a basic front-back bracket. The front of stack defender is guarding ALL cuts that come towards the disc, and the last back defender is guarding all cuts doing deep. NOTE: The reset defender or what is currently the #4 defender may be playing on the break side to prevent that easy option.
This biggest complication with a bracket is that there is no way to throw around either bracketing defender. It may seem like the area between is "wide open", however not only can any of the other defenders in the stack protect against such a throw, but throwing AT the sideline has its obvious dangers (over-throwing the disc out of bounds, for instance.
Instead, lets force the bracket to become active, rather than letting it guard the spaces we want to use. We mostly want to focus on the space closer to the disc. We choose to "challenge" this defender for two reasons: first, their viewable portion of the field is limited to the thrower and the and backfield, which makes them less knowledgeable about what is happening on the field. Second, shorter, quicker throws are more difficult to defend, and can confuse and disorient a defense/defender.
A cut from the front of the stack, to the open space, will force the front defender to guard that player or abandon the option. Assuming the defender is rational and not knowledgeable of what is directly behind them, they will cover that cut.
From here, the same cutter can either make a movement back to the center of the field (in the same manner as with a regular front of stack poach), or, the can draw that defender out so much that it actually releases the open field to in cuts.
If all else fails, always look to your reset. Nothing but really strong defensive effort can prevent a handler rush of short passes.
I encourage everyone to create their own bracket breaking offenses. They don't occur often, but they can be very disruptive to teams that aren't prepared.