Preheat oven to 325°F. Grease a muffin tin or line it with paper liners.
Peel and grate the carrots until you have 2 cups; set aside.
In a large bowl, whisk together 1 3/4 cups white whole-wheat flour, 1 1/2 teaspoons 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 in the grated carrots.
Pour the wet mixture into the dry ingredients. Using a spatula, gently fold until just combined — stop as soon as no large streaks of flour remain.
Divide the batter evenly among the prepared muffin cups, filling each about three-quarters full.
Bake for 25 to 30 minutes, or until a toothpick inserted in the center of a muffin comes out clean or with a few moist crumbs.
Let the muffins cool in the pan for about 5 minutes, then transfer them to a wire rack to cool before serving.