In a large bowl, combine the flour, brown sugar, cinnamon, baking powder, baking soda and salt. Stir together. In a small bowl, beat the eggs, Greek yogurt, orange juice, coconut oil and vanilla. Stir into the dry ingredients just until moistened. Fold in the carrots.
Transfer to two greased 8-in. x 4-in. loaf pans. Bake at 350° for 55-60 minutes or until a toothpick comes out clean. Cool for 10 minutes before removing from pans to wire racks.
Just before serving, make the glaze by whisking together cream cheese, milk, and confectioner's sugar in a small bowl. Drizzle over loaves.