Preheat oven to 350 degrees Fahrenheit.
In a mixing bowl, combine quick oats, flour, sugar (or cane juice crystals), cornstarch, baking powder, cinnamon, and salt.
Chop about 1/2 of a medium apple into 1/4 inch pieces. Measure 1/3 cup of finely chopped apple, and add apple pieces to mixing bowl.
Mix oil and nondairy milk together in a measuring cup, then pour into mixing bowl with dry ingredients. Stir until well combined.
Drop 12 heaping tablespoon-sized mounds onto a parchment-lined (or silicon-lined) cookie sheet. If you prefer smaller cookies, you can level off your tablespoons of dough, and make about 15 cookies.
Bake for 15-16 minutes, or until edges of cookies are slightly browned. (If you're making 15 smaller cookies, bake for 12-13 minutes.)
Allow to cool for 5 minutes before removing from pan.