Preheat the oven to 350°F (175°C). Line the bottom of a 9×5-inch loaf pan with parchment paper and lightly grease the sides.
In a medium bowl, whisk together the flour, baking powder, baking soda, poppy seeds, and salt.
In a large bowl, beat together the sugar and melted butter (or oil). Whisk in the Greek yogurt, eggs, lemon zest, and vanilla until smooth.
Gently fold the dry ingredients into the wet mixture just until incorporated. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top. Bake for 55 minutes to 1 hour, or until a toothpick inserted in the center comes out clean.
Remove from the oven and let cool in the pan for 10 minutes. Transfer to a wire rack to cool completely.
If using the glaze, whisk powdered sugar with lemon juice until smooth and drizzle over the cooled bread before slicing.