Preheat oven to 325°F and prep an 8.5×4″ loaf pan with butter and parchment paper.
Mix sugar and lemon zest until fluffy.
Add eggs, vanilla, and lemon extract, then whisk until light and ribbony.
Heat butter, oil, and milk until simmering, then slowly pour into the egg and sugar mixture while whisking.
Sift in flour, cornstarch, baking powder, baking soda, and salt. Gently fold until combined.
Add sour cream and lemon juice, fold gently.
Pour batter into the prepared loaf pan.
Optional: Pipe softened butter down the middle of the loaf.
Bake for 45-55 minutes, checking with a toothpick.
Let the cake cool for 20 minutes.
Prepare icing by mixing ingredients. Once the cake has cooled, spread the icing and garnish with lemon zest.
Slice in and enjoy!