Preheat the oven to 350 degrees F.
Heat 2 teaspoons olive oil in a large skillet set over medium heat. Add the onion to the pan. Season with ½ teaspoon salt. Cook for 10 minutes, reduce the heat to medium-low, and cook until the onions are golden brown, about 10 additional minutes.
Add 1 teaspoon olive oil to the onions, then stir in garlic and spinach leaves. Stir until the spinach is wilted and bright green, about 1 minute. Remove from the heat.
In a medium bowl, whisk together flour, baking powder, and salt. In a large bowl, combine eggs, lightly beaten, milk, and extra-virgin olive oil. Whisk well until combined.
Pour the flour mixture into the eggs mixture and stir until just combined. Do not overmix or the bread will become tough. Add the spinach mixture and myzithra cheese, and stir until just combined.
Butter a loaf pan. Spoon 1 tablespoon flour into the pan and tap the flour around the pan. Shake out the excess. Scoop the batter into the pan and smooth the top.
Bake until the top is light golden brown and a wooden skewer inserted into the center comes out dry, 35 to 40 minutes. Cool in pan for 15 minutes, then remove the bread from the pan, and cool on a wire rack. Slice and serve.