For the filling: Whisk together the chicken broth and flour in a microwave-safe 8-by-8-by-2-inch baking dish for an 1,100-watt oven or a 4-quart microwave-safe bowl for a 700-watt oven, until there are no lumps. Stir in the onions, celery, butter, thyme sprig, 3/4 teaspoon salt and a few grinds of pepper. Cover tightly with plastic wrap; cut a small slit in the center with the tip of a paring knife to vent excess steam. Microwave on high (at 100 percent power) for 5 minutes in an 1,100-watt oven or 8 minutes in a 700-watt oven.
Remove the dish from the microwave, and remove the plastic wrap (be careful to avoid the hot steam). Carefully whisk the broth mixture until there are no clumps of flour at the bottom. Put the dish back in the microwave, uncovered, and cook on high (at 100 percent power) until the broth is bubbly and thick, 5 minutes in an 1,100-watt oven or 8 minutes in a 700-watt oven.
For the dough: Meanwhile, in a medium bowl, whisk together the flour, cornmeal, baking powder and salt. Add the milk and oil in the center, and stir everything together with a fork until the dough just comes together (it will be sticky and wet).
To assemble: Remove the dish from the microwave. Remove and discard the thyme sprig, and whisk the broth mixture again. Stir in the shredded chicken and frozen peas and carrots. Arrange rounded teaspoons of the dough (about 16 dumplings) about 1/2 inch apart along the perimeter of the dish or bowl. Grind a little pepper over each dumpling.
Cover the dish tightly with a new piece of plastic wrap; cut a small slit in the center. Microwave on high (at 100 percent power) until the dumplings are puffed and a toothpick inserted in the center comes out clean, 6 minutes in an 1,100- or a 700-watt oven. If they are not cooked through, microwave them again in 30-second increments, testing with a toothpick after each.
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