Whisk white whole-wheat flour, all-purpose flour, 2 teaspoons cinnamon, baking powder, baking soda and salt in a medium bowl.
Beat 1 cup sugar, oil and butter in a mixing bowl with an electric mixer on high until smooth, scraping down the sides. Add eggs and vanilla and beat until smooth, scraping down the sides. Add the flour mixture and mix on low speed until just combined.
Place half the dough on a large piece of plastic wrap and shape into a 10-inch log (it’s OK if it’s not perfectly round). Repeat with the remaining dough. Wrap and freeze until just firm, about 45 minutes. Reroll the logs to make them rounder and return to the freezer until very firm, at least 1 hour more.
Preheat oven to 350°F. Line a baking sheet with parchment paper or a silicone mat.
Remove one roll of dough at a time from the freezer and let stand at room temperature for 5 minutes. Unwrap the dough and slice crosswise into 1/4-inch-thick rounds, turning the dough a quarter turn after each slice to help keep the cookies round. Place 1/2 inch apart on the prepared baking sheet. If your cookies aren’t as round as you want them to be, shape the dough with your fingers. Combine the remaining 1 teaspoon each cinnamon and sugar in a small bowl and sprinkle each cookie with a little.
Bake 8 minutes for soft cookies or 10 minutes for crisp cookies. Transfer to a wire rack to cool completely. Repeat with the remaining roll of dough, if desired.
Tip: White whole-wheat flour is made from a different variety of wheat than traditional white flour. It uses the whole grain, so it has almost the same nutrients as regular whole-wheat flour. But it has a milder taste that is more like white flour, making it a popular choice for cookies, muffins, and other baked goods.