Preheat oven to 350°F. Line two baking sheets with parchment paper.
Whisk flour, baking powder, baking soda, salt, and poppy seeds in a bowl.
Beat softened butter, granulated sugar, and brown sugar until pale and fluffy, about 2 minutes.
Mix in beaten eggs, vanilla, orange zest, and orange juice until smooth.
Stir in dry ingredients on low just until no dry streaks remain. Do not overmix.
Scoop 1½-tablespoon portions onto sheets, spacing about 2 inches apart.
Bake 10–12 minutes, until edges are set and centers look just dry.
Cool on the sheet 5 minutes, then transfer cookies to a rack to cool completely.
Whisk confectioners' sugar with orange juice and a splash of milk until thick but pourable.
Drizzle glaze over cooled cookies and let set for about 15 minutes.