Prep the ingredients per the instructions above.
Mix the water and cucumber slices and refrigerate until ready to serve.
To make the cornbread, preheat the oven to 375°F (190℃). Grease a small baking dish with nonstick spray.
In a medium bowl, mix the flour, cornmeal, sugar, baking powder, and salt. In a separate bowl, beat the egg and mix it with milk and oil. Add the wet ingredients to the dry ingredients and stir until well combined.
Pour the cornbread batter into the greased baking dish and bake for about 20-25 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean. Set aside to cool before portioning.
In a large pot, melt the butter over medium-high heat. Add the chicken and cook until browned, about 5-7 minutes. Add the onion, carrot, and celery to the pot and cook until the vegetables are softened, about 5-7 minutes.
Add the chicken broth to the pot and bring it to a boil. Reduce heat to low and simmer for about 30 minutes, or until the chicken is tender and cooked through.
In a small bowl, mix the flour with water to make a slurry. Add the slurry to the pot and stir well to thicken the broth. Season with salt and pepper to taste.
To make the dumplings, mix the flour with baking powder and salt in a medium bowl. Add milk and stir until a soft dough forms. Roll the dough into small balls, about 1 inch in diameter.
Drop the dumplings into the simmering broth and cook for about 10-15 minutes, or until they are cooked through and tender.
Portion and serve with cornbread and cucumber water.