Cut chicken into 3/4-inch pieces. In a 4- or 6-quart pressure cooker combine chicken, desired vegetables, corn, garlic, 1/2 teaspoon salt, basil, mustard, 1/8 teaspoon black pepper, and vegetable broth or water.
Lock lid in place. Place pressure regulator on vent pipe (if you have a first-generation cooker). Over high heat, bring cooker up to pressure. Reduce heat just enough to maintain pressure and pressure regulator rocks gently; cook for 3 minutes.
While mixture cooks, in a small bowl stir together the 1/3 cup flour, cornmeal, baking powder, the 1/8 teaspoon salt, and dash black pepper. Combine the 1/4 cup milk and cooking oil; add to flour mixture, stirring just until combined.
Quick-release the pressure. Carefully remove lid.
In a small mixing bowl stir together the 1/4 cup flour and the 3/4 cup milk; add to the pressure cooker. Cook and stir over medium heat until thickened and bubbly. Drop dumpling batter from a tablespoon to make 4 mounds atop bubbling chicken mixture. Cover loosely (do not lock lid) and simmer for 10 to 12 minutes or until a wooden toothpick inserted near center of dumpling comes out clean. Makes 4 main-dish servings.