Prep your pan and oven: Heat the oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or lightly grease each cup.
Mix dry ingredients: In a large bowl, whisk flour, sugar, baking powder, baking soda, and salt. If using poppy seeds, whisk them in now.
Combine wet ingredients: In a separate bowl or large measuring jug, whisk eggs, milk, oil (or melted butter), lemon juice, lemon zest, and vanilla until smooth.
Bring the batter together: Pour the wet ingredients into the dry.Stir gently with a spatula until just combined. A few small lumps are fine. Do not overmix or the muffins will be tough.
Fill the muffin cups: Divide the batter evenly among the cups, about 3/4 full. For taller domes, rest the filled pan for 5–10 minutes before baking.
Bake: Bake for 16–20 minutes, or until the tops are lightly golden and a toothpick comes out with a few moist crumbs, not wet batter.
Make the lemon drizzle: While the muffins bake, stir the lemon juice and sugar together until the sugar starts to dissolve.No need to heat it.
Soak while warm: As soon as the muffins come out, poke each one a few times with a toothpick. Spoon 1–2 teaspoons of the lemon drizzle over each muffin so it soaks in. Let them cool in the pan for 5 minutes, then move to a rack.
Glaze (optional): Once the muffins are cool, whisk powdered sugar with just enough lemon juice to make a thick, pourable glaze.Drizzle over the tops and let it set.
Serve: Enjoy slightly warm or at room temperature. The flavor deepens by the next day.