Preheat oven to 400°. Line a rimmed baking sheet with foil; set aside. In a bowl, whisk 1/2 cup flour and broth; set aside. Lightly coat a large saucepan with nonstick cooking spray and heat over medium-high heat. Add the chicken and cook until it is lightly browned, about 3 minutes. Transfer chicken to a 13 x 9-inch baking dish and set aside.

Return the saucepan to medium heat and add oil. Add the leeks and carrots and sauté for 4 minutes, or until leeks are tender. Add the wine and simmer until it has evaporated, about 1 minute. Add the flour-broth mixture, milk, and remaining 1/4 cup flour, and simmer until thick and bubbly, about 2 minutes. Add the chicken, asparagus, peas, parsley and lemon zest, and return to a simmer. Cook, stirring frequently, until the chicken is just cooked through, about 4 minutes. Season with sage, thyme and black pepper and transfer to the baking dish.

Lay 1 sheet of phyllo dough on a clean work surface; cover the remaining phyllo sheets with a towel. Brush the phyllo sheet lightly with butter. Lay the phyllo on top of the filling. Repeat with remaining phyllo sheets and butter, loosely stacking the phyllo over the chicken filling. Transfer the pie to the prepared baking sheet and bake until the phyllo is deep golden brown and crispy, and the filling is bubbly, about 30 minutes. Garnish with fresh thyme sprigs, if desired.