Make biscuits: Preheat oven to 375ºF. Line a baking sheet with parchment. Mix flour, baking powder and salt in a bowl. Use a pastry cutter to cut in butter until mixture resembles coarse sand. Gently stir in all but 1 Tbsp. milk. Turn dough onto a lightly floured countertop, knead just to bring together; pat into a 1/2-inch-thick circle. Cut into 6 biscuits with a 3-inch cutter. Place on baking sheet, cover and chill.
Make filling: Whisk cream and cornstarch in a bowl. Melt butter in a large pan over medium heat. Sauté shallot until softened, about 3 minutes. Stir in broth, vegetables, chicken and salt; bring to a boil. Stir in cream mixture; cook, stirring, until thickened.
Transfer filling to an 11-by-7-inch baking dish; arrange biscuits on top. Brush biscuits with remaining 1 Tbsp. milk. Bake until biscuits are golden, 18 to 20 minutes. Let stand 5 minutes before serving.