Preheat the oven to 350°. Line an 8 x 5loaf pan, line parchment paper, leaving an overhang on the long sides, and lightly coat with nonstick spray.
Sift or whisk flour, baking powder, and salt in a medium bowl.
Work lemon zest into granulated sugar (I used my Kitchen Aid mixer to do this) in a large bowl until sugar starts to clump and the mixture is very fragrant about 1 minute.
Add eggs, oil, and vanilla and beat with the electric mixer on high speed until light and thick, about 4 minutes. Reduce the speed to low, mix in half of the dry ingredients, and mix in 3/4 cup yogurt.
Mix in remaining dry ingredients followed by 4 Tbsp. lemon juice and poppyseeds.
Scrape batter into the prepared pan and smooth the top.
Bake loaf until the top is golden brown and a tester inserted into the center comes out clean, 50–60 minutes. Transfer pan to a wire rack. Poke holes on top of the cake and brush 3 Tbsp. lemon juice over top. Let sit for 15 minutes, then run a knife around the sides to loosen and use parchment paper to lift the cake out of the pan and onto the rack. Remove parchment and let cool completely.
Whisk powdered sugar, remaining 1 Tbsp. yogurt, 1 Tbsp. lemon juice in a medium bowl until smooth and drizzle over the cake. Let sit until the glaze is set, about 30 minutes.
