What essential element is necessary for a successful pâte brisée?

Cold butter is essential for a successful pâte brisée because it contributes to the flaky texture that is characteristic of this type of pastry. When the cold butter is cut into the flour, it creates small pockets of fat. During baking, the water in the butter steams and expands, leading to the desired flakiness. This freshness and firmness of the butter help to prevent the dough from becoming tough, which can occur if the fat is warmed or melted. It's important to ensure that the butter remains cold throughout the mixing process to maintain the integrity and texture of the dough.

The other elements mentioned, such as high gluten flour, warm water, and active yeast, are not appropriate for pâte brisée. High gluten flour would create a more elastic dough, which is not desirable in this context. Warm water could lead to melting the butter and creating a tough pastry, while active yeast is irrelevant as pâte brisée is a type of pastry that does not require leavening.