Preheat the oven to 375F (190C).

On a lightly floured surface, roll out half the pastry and line a 10-1/2 inch (26.25cm).  Trim and crimp the edge.  Line the pastry with aluminum foil, fill it with pastry weights and bake it on the lowest rung of the oven until it is golden around the edges, about 15 minutes.  Remove the weights and paper, and continue baking until the bottom of the crust set and light golden, 5 to 20 more minutes. Remove the pastry from the oven and let it cool.  Leave the oven on.

Combine the chicken stock, bay leaf, and peppercorns in a small saucepan and bring to a boil over high heat. Remove from the heat, cover,  and set aside to infuse for 5 minutes.  Strain.

Melt the butter in a small saucepan over medium-high heat.  When the butter is melted, whisk in the flour and cook until the mixture bubbles. Continue cooking and whisking constantly for 2 minutes.  Pour the chicken stock into the mixture, whisking as you do, and cook until it has thickened.  Whisk in the cream and season to taste with plenty of salt, pepper, and a touch of nutmeg.  Set the cream sauce aside.

Bring the water to a boil in the bottom of a vegetable steamer.  Place the potatoes in the steamer basket, cover, and steam for 8 minutes. Add the broccoli, cover, and steam until the broccoli and the potatoes are tender, an additional 8 minutes.  Remove the steamer with the vegetables from the pan, and set aside.

Pour the olive oil into a medium skillet and set it over medium-high heat. Add the onions, stir, season with salt and pepper, and cook, stirring often, until they are golden, about 10 minutes. Add the garlic and continue cooking, stirring constantly, for about 1 minute. Remove them from the pan, return the pan to the heat and add the chicken or turkey.  Increase the heat so the meat sizzles merrily and cook, stirring constantly, until the meat is golden on all sides and just about cooked through, about 8 minutes. Remove from the heat.

Roll out the remaining pastry into a 12-inch (30cm) circle.

In a large bowl gently fold together the onions and garlic, the chicken or turkey, the vegetables, and the hard cooked eggs. Pour the cream sauce over all, and gently fold all the ingredients together, then turn them into the pre-baked pastry.  Cover with the round of pastry, tucking it around the ingredients and pressing the edges gently but firmly onto the baked pastry.  Crimp the edge.

Make several slits in the top of the pastry, place the pie on a baking sheet and slide the whole thing into the oven. Bake until the top pastry is golden, about 35 minutes. Remove from the oven and let sit for 10 minutes before serving.