With the rack in the middle position, preheat the oven to 200 °C (400 °F). Butter a 23 x 13-cm (9 x 5-inch) loaf pan.
In a skillet, soften leek in butter. Let cool.
In a large bowl, beat eggs with milk. Add bread and let soak for about 5 minutes. Add meat, cheese and cooled leek mixture. Mix thoroughly with your hands until mixture is smooth. Season with salt and pepper. Pour into the loaf pan. Bake for 1 hour and 15 minutes. Let rest for 15 minutes before slicing.
Meanwhile, in a skillet, brown mushrooms in butter. Sprinkle with flour and mix thoroughly. Add milk, broth and garlic and bring to a boil, whisking constantly. Simmer until sauce thickens. Adjust seasoning. Sprinkle with fresh thyme leaves, if desired.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.