In a medium bowl, whisk together the milk and eggs. In a separate bowl, sift together the baking powder, 1 1/2 cups of the flour and 1 teaspoon of the salt. Add the dry ingredients to the wet and mix until combined, being careful not to overmix. Set the dumpling batter aside.
In a medium pot, combine the stock, half-and-half, pepper, thyme, bay leaf and remaining 1/2 teaspoon salt and bring to a boil. In a small dish, whisk the remaining 2 tablespoons flour with 1/4 cup water. Whisk the flour mixture into the chicken stock mixture. Add the chicken and mixed vegetables and return to a boil. Using a tablespoon or a small ice cream scoop, drop scoops of the dumpling batter into the boiling liquid. Reduce the heat to a simmer and cook, uncovered, for 10 minutes. Cover and cook an additional 10 minutes. Garnish each serving with fresh parsley.