Preheat the oven to 350 degrees F. Lightly coat a loaf pan with cooking spray.
Heat 2 teaspoon of olive oil in a large nonstick skillet set over medium-high heat. Add the shallot and mushrooms, and cook until tender, about 3 minutes. Stir in the spinach, rosemary, ¼ teaspoon and pepper, and cook until wilted, about 1 minute. Remove from the heat.
In a medium-sized bowl, whisk together the flour, baking powder and salt. In a large bowl, whisk the eggs, then stir in the milk and ⅔ cup olive oil. Pour the milk mixture into the flour mixture and stir until just combined. Stir in the mushroom mixture and 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. Slice into 16 slices. Serve.