Heat 1 cup water in a small saucepan or a tea kettle over high until a thermometer registers 200°F, 2 to 3 minutes. Pour ¼ cup hot water into a medium-size heatproof bowl; discard remaining water. Stir tea leaves into water; cover and steep 5 minutes. Pour tea through a fine wire-mesh strainer, and return to bowl; discard tea leaves. Measure out 1 tablespoon steeped tea, and set aside. Stir poppy seeds into remaining tea in bowl, and let soak, covered, at room temperature, until slightly plumped, for at least 30 minutes or up to 12 hours.

Preheat oven to 375°F. Line a 12-cup muffin tray with muffin liners; set aside. Whisk together flour, granulated sugar, baking powder, baking soda, and salt in a medium bowl; set aside. Whisk together eggs, butter, milk, and lemon zest and juice in a large bowl until smooth. Add about one-third of flour mixture to butter mixture; stir and fold with a rubber spatula until almost incorporated. Repeat process with another one-third of flour mixture. Add final one-third flour mixture and soaked poppy seeds with any remaining soaking liquid to batter; fold until just incorporated.

Scoop batter into prepared muffin tray, about ⅓ cup per well. Bake in preheated oven until muffins are golden brown and a wooden pick inserted in centers comes out mostly clean with a few moist crumbs, 15 to 18 minutes. Let muffins cool to room temperature in tray on a wire rack, about 30 minutes.

Whisk together powdered sugar, honey, and reserved 1 tablespoon tea in a small bowl until smooth. Drizzle glaze over muffins; let stand 10 minutes before serving.