Preheat the oven to 375°F. Line muffin tin with cupcake liners. Set aside.
In a large bowl, whisk together the the flour, cornstarch, baking powder, salt, lemon zest, and poppy seeds.
In the bowl of a stand mixer (or in a large mixing bowl and using a hand mixer), cream the butter until fluffy and light, about 3 minutes. Scrape down the sides with a spatula as needed.
Add the sugar and beat with the butter for 3 to 4 minutes.
Add the eggs, vanilla, milk, and lemon juice. Mix together just until the ingredients are well blended, about 1-2 minutes.
Gradually add the dry ingredients to the wet ingredients just until the ingredients are all incorporated.
Scoop batter into the prepared muffin tin. You will likely have enough for about 15-17 cupcakes, so you will either need to use two muffin tins or bake one batch at a time.
Bake at 375°F for 5 minutes. Then turn down the heat to 350°F and bake for an additional 15-20 minutes, or until a toothpick inserted into the center of a cupcake comes out clean. While the cupcakes are baking, make the frosting.
Make the frosting
In the bowl of a stand mixer, cream the butter for 2-3 minutes until light and fluffy. Add the powdered sugar, cream, vanilla, and lemon juice. If you want thicker frosting, add a little more powdered sugar until the frosting reaches your desired consistency.
Assemble
Allow the cupcakes to cool in the pan for 5 minutes, then transfer to a wire rack to cool completely before frosting.
Notes
Makes about 17 cupcakes. Storage: Store unfrosted cupcakes in an airtight container at room temperature for up to 5 days. Store frosted cupcakes in an airtight container in the refrigerator for up to 4 or 5 days. Allow refrigerated cupcakes to sit at room temperature for a minute or two before eating. For more lemon flavor in the frosting: Add 1 teaspoon of fresh lemon zest to the frosting and mix until well incorporated.