Heat oven to 425°F (218°C). Line a 12-cup muffin tin with paper liners; coat liners with nonstick spray or oil.
Whisk together 2 cups (240g) whole-wheat flour, 2 tablespoons cornstarch, 2 teaspoons ginger, 1 ½ teaspoons cinnamon, 1 teaspoon baking powder, ½ teaspoon baking soda, ½ teaspoon salt, and heaping ¼ teaspoon nutmeg in a medium bowl, set aside.
Whisk together 1 cup (233g) Greek yogurt, ⅓ cup (80g) oil, ½ cup (180g) honey, 2 eggs, and 2 teaspoons vanilla in a large bowl until smooth.
Add flour mixture to yogurt mixture and using a rubber spatula, mix until mostly incorporated but some pockets of flour remain. Gently fold 2 cups (178g) shredded carrots into batter.
Divide batter (it will be thick) between prepared muffin cups, about ⅓ cup per muffin cup. Combine ¼ cup pecans and 1 tablespoon turbinado sugar and sprinkle evenly over cups of batter.
Bake muffins 5 minutes at 425°F (218°C) then, keeping muffins in oven, reduce oven temperature to 350°F (177°C) and bake until a toothpick inserted in the centers comes out clean, 16–18 minutes more. (Total bake time is about 21–23 minutes.)
Transfer muffin tin to a wire rack and cool 5 minutes, then transfer muffins from pan to wire rack to cool completely.