Preheat the oven to 350 degrees F. Lightly coat a loaf pan with cooking spray.
Heat 1 ½ teaspoon of oil in a large nonstick skillet set over medium-high heat. Add the shallot and cook, stirring occasionally, until tender and golden brown. Set aside.
In a medium-sized bowl, whisk together the flour, baking powder and salt. In a large bowl, whisk the eggs, then sir in the milk and ⅔ cup olive oil. Pour the milk mixture in to the flour mixture and stir until just combined. Stir in the cooked shallots, zucchini and feta cheese.
Transfer the batter to the prepared loaf pan. Bake until a toothpick inserted in the center comes out clean, about 35 minutes. Let the bread rest in the pan for 10 minutes, then carefully turn upside down to release the bread from the pan. Cool on a rack. Cut into 16 slices, or as needed. Serve. Store any remaining bread in the refrigerator, wrapped in plastic wrap.