Vegetable Pot Pie

Steps

1. Preheat the oven to 400°F (200°C). Peel the potatoes and cut them into 5/8-inch (1.5 cm) cubes. Slice the carrots into 1/2-inch (1 cm) rounds, cut the celery into 1/2-inch (1 cm) pieces and quarter the mushrooms. Chop the onion, mince the garlic and strip the thyme leaves. Rinse and drain the white beans.
2. Melt the butter over medium heat in a large deep skillet or Dutch oven. Add the onion, carrots, celery and a pinch of fine salt. Cook for 6 minutes, stirring, until the onion is translucent and the carrots look glossy.
3. Add the mushrooms and raise the heat to medium-high. Cook for 5 minutes: they release their water, it cooks off, then they start to brown. Add the garlic and thyme and stir for 1 minute.
4. Sprinkle the flour over the vegetables and stir constantly for 2 minutes: it soaks up the butter and loses its raw taste. The bottom of the pan should stay pale and smell like cookies.
5. Pour in the vegetable broth a little at a time, stirring to prevent lumps, then 380 ml of the milk; save the remaining 20 ml for the egg wash. Add the potatoes, 1 tsp of fine salt and the black pepper. Bring to a simmer and cook for 10 to 12 minutes over low heat, stirring often because the sauce catches, until the tip of a knife slides into the potatoes without them falling apart.
6. Off the heat, stir in the white beans and the still-frozen peas and corn, which bring the temperature down, then the Dijon mustard. Taste and adjust the salt: the gravy should be thick, it will loosen in the oven. Pour the filling into an 11 x 9-inch (28 x 22 cm) baking dish and let it cool for 10 minutes.
7. Unroll the puff pastry and roll it into a 13 x 10-inch (32 x 26 cm) rectangle, so it overhangs the dish by 3/4 inch (2 cm) on each side. Lay it over the filling and press the edge against the side of the dish. Beat the egg with the reserved 20 ml of milk and brush it over the pastry, without letting it drip onto the cut edges, which would glue the layers together. Cut 4 slits, 1 1/4 inches (3 cm) long, in the center to let steam escape.
8. Set the dish on a baking sheet to catch any drips and bake for 30 to 35 minutes at 400°F (200°C), until the pastry is fully puffed and deep golden brown and the sauce is bubbling through the slits.
9. Let it rest for 10 minutes out of the oven: the gravy firms up and won't run across the plate. Serve with a big spoon, breaking through the pastry so every portion gets some crust.