Preheat the oven to 350F (180C). Line the muffin pan with cupcake liners.

Place the sugar in a medium-sized bowl and zest the lemon directly onto the sugar. Once you have about 2 tablespoons, use your fingers to rub the sugar and lemon zest together until the sugar turns yellow and is very fragrant. Juice the lemons until you have 1/2 of lemon juice.

Place the sugar, the flour, the salt and the baking powder in the bowl of a stand mixer. With the paddle attachment mix the dry ingredients on medium-low for 30 seconds to thoroughly combine the dry ingredients. Add the butter and mix on medium speed until the butter is thoroughly incorporated and the mixture is a little crumbly, about 1 minute. Add all the milk and mix on medium speed until the milk is incorporated and the batter looks creamy. Be careful not to overmix. Scrape the sides and bottom of the bowl.

Whisk the eggs and add the eggs to the batter. Mix on medium speed until the eggs are incorporated. Add the lemon juice and mix on medium speed just until incorporated. Scrape the sides and bottoms of the bowl and fold the batter by hand to ensure all the butter is mixed together.

Divide the batter evenly between the 12 cups of the muffin pan, about 65 grams each. Each muffin tin should be about 2/3 full.

Bake the cupcakes for 20-22 minutes until they are done. Remove the cupcakes from the oven and let them cool in the pan for 10 minutes before removing the cupcakes from the pan to a cooling rack. Allow the cupcakes to cool completely before frosting them.

If making the cupcakes one day in advance before frosting them, store the cupcakes in an airtight container at room temperature.

Sift the flour and cornstarch into a 3 or 4-quart saucepan. Add the sugar and salt and whisk for 30 seconds to thoroughly combine the ingredients. Whisking constantly, slowly add the milk until it is incorporated and there are no lumps. Add the lemon juice and whisk to incorporate.

Place the mixture over medium-high heat and whisk constantly until the mixture has thickened and you see a 2 or 3 bubbles pop on the surface.

Pour the mixture into the bowl of a stand mixture. With the whisk attachment mix the flour mixture on medium low speed for 10-12 minutes until the mixture reaches room temperature.

In a medium-sized bowl bowl cream the butter by hand with a spatula until it looks creamy. Add all the butter to the flour mixture and mix on medium-high speed until the mixture is fluffy and creamy, 5-6 minutes.

Frost the cupcakes and serve.