Preheat the oven to 350ºF and spray a 9x5-inch loaf pan with cooking spray. Then, line with parchment paper.
In a medium bowl combine the flour, baking soda, baking powder, poppy seeds, salt, and lemon zest. Whisk the ingredients together and set aside.
Next, add the egg to a large bowl and whisk. Add the brown sugar and whisk until combined.
Slowly drizzle the oil into the bowl while whisking.
Add the applesauce, lemon juice, milk, and vanilla to the egg mixture and whisk until combined.
Add the dry ingredients to the wet ingredients and mix until combined. Be sure not to overmix.
Transfer the batter into the lined loaf pan.
Bake the poppyseed bread for 15 minutes, turn the bread in the oven, cover with a tin foil tent, and bake for an additional 20-22 minutes. Be sure the bread is fully cooked by sticking a toothpick into the center -- if it comes out clean, it’s done.
Meanwhile, prepare the lemon glaze by combining the powdered sugar, lemon juice, water, and lemon zest into a bowl. Mix until smooth.
Remove the bread from the oven and let cool for 5-10 minutes before removing it from the loaf pan. Allow the bread to cool on a cooling rack before drizzling the glaze on top of the bread.
Slice and serve.