In a small bowl, combine 1 tablespoon ground flaxseed with 2 1/2 tablespoons water. Stir well and let sit for 5-10 minutes until thickened and gel-like.
In a large mixing bowl, whisk together 1/2 cup plus 3 tablespoons cane sugar and 1/2 cup brown sugar until combined. Add the flaxseed mixture, 1/3 cup plus 1 tablespoon olive oil, and 2 teaspoons vanilla extract. Whisk until smooth and creamy.
Using a microplane or fine grater, zest the peel of 1 navel orange directly into the wet ingredients. Stir to distribute the zest evenly throughout the batter.
In a separate bowl, sift together 1 cup plus 6 tablespoons all-purpose flour, 2 teaspoons cornstarch, 1/2 teaspoon baking powder, 1/4 teaspoon baking soda, and 1/2 teaspoon kosher salt.
Add the dry ingredients gradually into the wet mixture. Fold gently with a spatula until just combined. Avoid overmixing.
Cover the dough and refrigerate for at least 30 minutes.
Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone mat.
Using a tablespoon or cookie scoop, drop dough onto the prepared sheet, spacing about 2 inches apart. Bake for 10-12 minutes, until edges are lightly golden but centers remain soft.
Let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely. Enjoy warm or at room temperature.