Preheat oven to 350°F (175°C). Grease mini bundt pan.
Whisk flour, baking powder, salt, and poppy seeds in a bowl.
Beat butter and granulated sugar until light, about 2 minutes.
Add eggs one at a time, beating after each addition.
Mix in lemon zest, lemon juice, and vanilla.
Alternate adding flour mixture and milk, beginning and ending with flour. Fold gently.
Spoon batter into pan, filling each 2/3 full.
Bake 12–15 minutes or until a toothpick comes out clean. Cool 10 minutes, then invert.
Whisk powdered sugar with lemon juice to make glaze. Drizzle over cooled cakes.