How to Make It
In a food processor, pulse 1 1/4 cups of the flour, 1/2 teaspoon of sea salt and sugar. Add the butter and shortening and pulse till the mixture resembles wet sand. Add cold water 1/4 teaspoon at a time (up to 1 1/2 teaspoons), and pulse until the dough comes together in a ball. Remove the dough from the processor and wrap it tightly in plastic wrap. Let the dough rest in the refrigerator for 1 hour.
Meanwhile, preheat the oven to 400°. Season the chicken with 1/4 teaspoon of sea salt and 1/8 teaspoon of freshly ground pepper. In a medium nonstick frying pan, heat 1 teaspoon of the extra-virgin olive oil over medium high heat. Add the chicken breasts and cook for 1 minute. Turn the chicken, cover the pan, reduce the heat to low and cook for 8 minutes. Remove from the heat and let it sit, covered, for 10 minutes, then shred the chicken with 2 forks.
In a large nonstick frying pan, heat the remaining 2 tablespoons of extra-virgin olive oil over medium high heat. Add the onions and cook for 5 minutes, until they soften and begin to brown. Add the diced potato and cook for 5 minutes. Add the carrot, red pepper and cauliflower and cook, stirring frequently for 5 minutes.
Add the brandy to the pan and use a wooden spoon to scrape up any browned bits on the bottom. Sprinkle the remaining 1/2 cup of flour over the vegetables and mix well. Add the water and stir until the sauce thickens, about 2 minutes.
Remove from the heat and stir in the shredded chicken, heavy cream and frozen peas. Season generously with sea salt and freshly ground pepper. Transfer the mixture to an 8-by-10-inch baking dish.
Remove the dough from the refrigerator and place it between 2 sheets of parchment paper. Flatten it with the palm of your hand, then roll the dough out to a 10-by-12-inch rectangle. Use the parchment paper to transfer the dough onto the baking dish. Crimp the edges of the dough or let them hang for a more rustic look. Place the baking dish on a baking sheet and bake for 35 to 45 minutes, until the sauce is bubbling hot and the pie crust is lightly browned. Allow the casserole to cool for 10 minutes before serving.