Preheat oven to 350 degrees F.
In a large bowl, whisk together the flour, baking powder, baking soda, poppy seeds, lemon zest and salt, set aside. In a medium bowl, whisk together the Greek yogurt, eggs, olive oil, honey, lemon juice, and vanilla, mixing until all combined.
Pour the wet ingredients into the dry ingredients and gently mix with a spatula until just combined. Make sure not to overmix, a few lumps are totally fine and help keep the bread tender.
Pour the batter into a prepared 9x5-inch loaf pan line with parchment paper or sprayed with nonstick spray. Bake in the oven for 40 to 45 minutes, or until a toothpick inserted in the center comes out clean.
Let the bread sit for 10 minutes, then remove from the pan and let it cool completely on a wire rack.
In a small bowl, whisk together the powdered sugar, lemon juice and zest, mixing until smooth. Drizzle over the cooled bread, slice and enjoy!