Grind the oatmeal and pecan pieces in a food processor until they resemble cornmeal--reasonably fine but with some texture. Whisk the whole wheat flour, cornstarch, ginger, salt and baking soda together in a medium bowl. Whisk in the oat/nut mixture.
In another medium bowl, beat the butter with an electric mixer until smooth and light, about 1 minute. Gradually add the granulated and light brown sugar; continue beating until evenly combined, about 3 minutes more. Add the vanilla and the egg.
Mix in the dry ingredients to make a textured dough. Line a 1 1/2-quart loaf pan or 3 mini loaf pans with plastic wrap and pack dough into the bottom half of the pan. Press to level off the dough. Lay a piece of plastic wrap on top and refrigerate until completely firm, about 2 hours.
Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper or silicone mats.
Remove dough from the pan and unwrap. Slice dough in half lengthwise if using a large pan. Slice each log crosswise into 1/4-inch thick cookies. Place the cookies about a 1-inch apart on the prepared pans. Bake until golden brown, 15 to 18 minutes. Transfer cookies to a rack to cool and crisp. Serve.
Store cookies in a tightly sealed container for up to 1 week.
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