Preheat oven to 325 degrees F. Coat a 8½ by 4½ -inch loaf pan with cooking spray.
In a medium-sized bowl, whisk the 2 eggs. Stir in the goat milk yogurt, applesauce, olive oil and vanilla extract.
In a large bowl, whisk together the whole wheat flour, 1 cup all-purpose flour, brown sugar, lemon zest, baking powder, baking soda, ground ginger and salt.
Pour the yogurt mixture into the flour mixture. Stir to combine.
In a small bowl, stir together the frozen berries and the remaining 2 teaspoons all-purpose flour.
Stir the flour-coated berries into the batter and mix until just combined.
Pour the batter into prepared pan and level with a spatula.
Bake until a toothpick inserted in the center comes out with only a few crumbs attached, 55 to 60 minutes. Let the bread sit in the pan for 10 minutes.
Run a knife around the outside and turn the pan upside down to release the bread. Let cool on a wire rack, then slice and serve.