Preheat the oven to 325°F. Grease a muffin tin or line it with paper liners.
In a large bowl, whisk together 1 3/4 cup white whole-wheat flour, 1 1/2 teaspoon baking powder, 1/2 teaspoon baking soda, and 1 teaspoon ground ginger.
In a separate bowl, lightly beat 2 eggs. Add 1/2 cup honey, 1/4 cup olive oil, 1 tablespoon vanilla extract, and 1 cup plain Greek yogurt; whisk until smooth.
Stir 2 cups peeled and grated carrots into the wet mixture.
Pour the wet ingredients into the dry ingredients and gently fold with a spatula or wooden spoon until just combined—do not overmix.
Spoon the batter into the prepared muffin tin, filling each cup about three-quarters full.
Bake at 325°F for 25–30 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Remove muffins from the oven and let them cool in the pan for about 5 minutes, then transfer to a rack to cool completely before serving.