In a food processor, finely chop the mushrooms. Transfer to a bowl and set aside.
Coarsely chop the chickpeas in the food processor.
In a pot over medium heat, soften the onions, leek and garlic in the oil. Add the mushrooms and cook for 5 minutes. Season with salt and pepper. Add the wine, mustard and spices. Simmer until the wine has evaporated. Add the chickpeas and mix well. Adjust the seasoning. Set aside.
With the rack in the bottom position, preheat the oven to 350°F (180°C).
In a large bowl, combine the flour and salt.
In a measuring cup, combine the water and honey. Add the oil. Pour over the dry ingredients and stir with a fork until the flour is just moistened. Shape the dough into 2 discs, each about 1 inch (2.5 cm) thick.
Roll out one disc at a time between 2 sheets of parchment paper. Line a 9-inch (23 cm) pie plate with one circle of dough. Spread the filling evenly in the pie shell. Cut a few slits in the second circle of dough, then place over the filling. Seal tightly by crimping the edges of the dough with a fork or your fingers. Brush with milk.