In a large bowl, whisk together the flour, baking powder, baking soda, salt, and poppyseeds. Set aside.

In a medium sized bowl, rub together the granulated sugar and lemon zest for about a minute, until the sugar clumps slightly and is thoroughly mixed.

In the same bowl, add the melted butter, vegetable oil, and eggs to the sugar and whisk to combine. Pour in the lemon juice, vanilla extract, lemon zest, milk, and sour cream and mix until smooth.

Pour the wet ingredients into the dry and fold until just combined. Cover the bowl with plastic wrap or a towel and allow to rest for 1 hour (you can skip this step, but you won't get as much of a rise on your muffins).

Preheat an oven to 425°F and line a muffin tin. Scoop the rested muffin batter into the muffin liners, filling nearly to the top. If desired, sprinkle with coarse sugar before baking, then place in the oven.

Bake the muffins for 5 minutes at 425°F, then decrease the oven temperature to 375°F without opening the oven and bake for 8-15 more minutes, until a toothpick inserted comes out clean.

Set the muffins aside to cool and prepare the glaze. In a bowl, mix together the powdered sugar and lemon juice until a thin icing is formed. If it is too loose, add more powdered sugar; if it's too stiff, add more lemon juice. Drizzle the glaze over each muffin and allow to set. Enjoy!