Preheat oven to 400°F.
Heat butter in a large sauté pan over medium heat. Add the leek, onion, carrots, and mushrooms with a pinch of salt and cook for 8-10 minutes until softened and slightly golden.
Add the garlic and cook for 1 minute.
Sprinkle in the flour and stir to coat everything well. Cook for 1-2 minutes to get rid of the raw flour taste.
Slowly pour in the chicken broth, stirring constantly, then add the milk. Simmer for 15-20 minutes uncovered, stirring occasionally, until it thickens to a gravy-like texture.
Stir in the shredded chicken, peas, corn, Dijon, lemon juice, thyme, salt, and pepper. Taste and season with more salt and pepper as necessary.
Transfer everything to your roasting pan and spread evenly.
Prepare the biscuit dough according to the package instructions, then add dollops of dough over the top of the chicken pot pie filling.
Bake for 20-30 minutes, until golden and bubbling.
Let sit for 10 minutes before serving.