Preheat your oven to 350°F (175°C). Line a 9×5-inch loaf pan with parchment paper, leaving an overhang on the sides.
In a medium bowl, whisk together the flour, poppy seeds, baking powder, and salt.
In a large bowl, beat the softened butter and sugar with an electric mixer on medium speed until light and fluffy, about 3-4 minutes.
Add eggs one at a time, beating well after each addition. Stir in the Greek yogurt, lemon juice, lemon zest, and vanilla extract.
Gradually add the dry ingredient mixture to the wet ingredients, alternating with milk, beginning and ending with the flour mixture. Mix on low speed just until combined.
Pour the batter into the prepared loaf pan and smooth the top with a spatula. Bake for 50-55 minutes, or until a toothpick inserted into the center comes out clean. If the top begins browning too quickly, tent with aluminum foil.
While the loaf cools, prepare the glaze by whisking together powdered sugar, lemon juice, and zest in a small bowl until smooth.
Once the loaf has cooled in the pan for 15 minutes, use the parchment overhang to lift it out and transfer to a wire rack. Allow it to cool completely before drizzling with the lemon glaze.
Let the glaze set for about 10 minutes before slicing and serving.