Combine the first five ingredients in a mixing bowl and stir together.
Make a well in the center of the dry ingredients. Pour in the applesauce, oil, and
nondairy milk. Stir until well combined, adding more nondairy milk if needed to make a smooth, slightly stiff batter. Stir in the corn kernels and the chilies and cheese, if desired.
Pour the batter into an oiled 9 × 9-inch baking pan or divide among a foil-lined 12-cup muffin tin. Bake for 20 to 25 minutes, or until the top is golden and a knife inserted in the center comes out clean.
Let cool until just warm. Cut the pan bread into 12 sections; for muffins, transfer them to a serving plate, leaving them in the foil liners.