Preheat the oven to 425°F. Line a 12-cup muffin pan with liners and set aside.
Mix the dry ingredients: In a large bowl, whisk together the flour, poppy seeds, baking powder, baking soda, and salt. Set aside.
In a separate bowl, combine the sugar and orange zest. Rub them together with your fingers until the sugar is fragrant and the zest releases its oils.
Add the eggs, oil, sour cream, milk, orange juice, and vanilla extract to the sugar mixture and whisk until well combined.
Add the dry ingredients to the wet mixture and stir gently just until combined. Don’t overmix the batter.
Divide the batter evenly among the muffin cups, filling the liners nearly to the top.
Bake for 5 minutes at 425°F, then reduce the oven temperature to 350°F (keep the muffins in the oven) and bake for 12–15 minutes, or until a toothpick inserted in the center comes out clean.
Cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.
Make the orange icing: In a small bowl, whisk together the powdered sugar, orange juice, and orange zest. Add 1 tablespoon of juice at a time until the icing is thick but pourable.
Drizzle the icing over the cooled muffins and let it set for a few minutes before serving.