Prepare the Baking Station: Position oven racks in the upper and lower thirds of your oven and preheat to 375°F (190°C). Line your two half-sheet pans with parchment paper.
Combine Dry Ingredients: In the small bowl, whisk together the white whole-wheat flour, rolled oats, ground flaxseed, baking powder, cinnamon, nutmeg, and salt.
Combine Wet Ingredients and Sugar: In the large mixing bowl, beat the avocado oil, unsweetened applesauce, and packed brown sugar with an electric mixer on medium speed for about 1 minute until well combined.
Incorporate Egg and Vanilla: Add the egg and vanilla extract to the sugar mixture. Beat on low speed until just combined, scraping down the sides of the bowl with a spatula as needed.
Form the Dough: Pour the dry ingredient mixture into the wet ingredients. Mix on low speed until a cohesive dough forms. Be careful not to overmix. Gently fold in the unsweetened dried cranberries with the silicone spatula.
Portion and Bake: Drop rounded tablespoons of the cookie dough about 2 inches apart onto the prepared pans, placing 8 cookies on each pan. Bake both pans at the same time for 9 to 11 minutes, rotating the pans top-to-bottom and front-to-back halfway through. The cookies are done when the edges are set and lightly golden.
Cool and Set: Remove the pans from the oven and let the cookies rest on the hot pans for 3 minutes to firm up. Afterward, carefully transfer them to a wire rack to cool completely.