In a stand mixer with a paddle attachment, blend the eggs, sugar, vanilla extract vegetable oil and milk. Mix until the eggs are broken up and distributed evenly throughout the wet ingredients.

Add the baking powder, poppy seeds, salt and flour to the bowl and mix until a nice smooth batter has formed.

Line a muffin tray with paper muffin liners or simply grease a muffin pan with butter or cooking spray. Scoop the muffin batter into the muffin tin filling each cup about 3/4 of the way up.

While the muffins are baking, mix the powdered sugar and lemon juice in a small bowl to make the lemon icing. Set aside to use after the muffins have cooled.

Bake the muffins in a 350 ̊F oven for about 20 minutes. The muffins should be firm to the touch and no longer be liquid in the center. Once the muffins have cooled enough to handle, dip the tops into the lemon icing or use a spoon to pour the lemon icing over the top of the muffins.

Serve immediately or store at room temperature for up to a week.