2 tbsp. flour, plus more for rolling
1 sheet (14 to 17.3 oz.) frozen puff pastry, thawed (I like Dufour)
1 rotisserie chicken
4 tbsp. butter
1 carrot, peeled and cut into 1/4-inch pieces
½ bulb fennel, chopped into 1/4-inch pieces
1 large shallot or small onion, chopped
1 stalk celery with leafy top, chopped
1 small bundle green asparagus or white asparagus—bottom thirds of stalks trimmed and tops thinly sliced on an angle
2 large cloves garlic, chopped
1 rounded tsp. (about 1/3 palmful) herbes de Provence
Salt and finely ground white or black pepper
½ cup white wine
2 cups chicken stock
1 small container (1.5 oz.) or about 2 tbsp. veal or chicken demi-glace (optional)
½ cup heavy cream
3 tbsp. fresh tarragon leaves (stripped from a few sprigs), chopped
2 tbsp. Dijon mustard (I like Maille)
A little freshly grated nutmeg, to taste
½ cup frozen peas
Preheat the oven to 400°.
Line a baking sheet with parchment paper. Lightly flour a work surface and rolling pin. Unfold the pastry. Gently roll out the pastry a bit to smooth out the creases. Cut the pastry horizontally in half, then cut each half crosswise in half. Cut each section into 2 to 3 strips and arrange on the parchment paper. In a small bowl, beat the egg with about 2 tsp. water. Brush the pastry with the egg wash. Bake the puff pastry strips until puffed and deep golden, about 20 minutes.
Pull or chop the chicken meat into bite-size pieces. (Reserve the skin and bones for stock.)
Meanwhile, in a deep skillet, melt the butter over medium to medium-high heat. Add the carrot, fennel, shallot, and celery and cook, stirring often, until softened, about 5 minutes. Add the asparagus, garlic, and herbes de Provence; season with salt and pepper. Cook until the asparagus starts to soften, about 3 minutes more. Stir in 2 tbsp. flour. Whisk in the wine and cook until absorbed, about 30 seconds. Add the stock and the demi-glace (if using) and stir until dissolved. Cook, stirring often, until the sauce thickens, about 2 minutes. Stir in the cream and reduce heat to low. Add the tarragon, Dijon, and nutmeg. Stir in the chicken and peas. Cook until the chicken is heated through, about 2 minutes.
Transfer the chicken filling to a 3-quart casserole dish. Top with the puff pastry strips.