Heat oven to 350°. Whisk flour, poppy seeds, baking powder, and salt in a bowl; set aside. Beat sugar, butter, and vanilla in a bowl with a hand mixer until pale and fluffy. Add eggs one at a time, beating after each; mix in dry ingredients. Form dough into a disk; halve. Roll each half on a floured work surface until ¼″ thick; chill. Cut out 1½″-wide diamonds from dough; transfer to paper-lined rimmed baking sheets. Bake until golden, 12–15 minutes. Meanwhile, boil honey and ⅓ cup water in a saucepan. Place all cookies in a single layer on one of the baking sheets; pour over honey. Let sit for 10 minutes before serving.