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Step 1
Preheat your oven to 350 degrees F. Line a 9x5-inch loaf pan with parchment paper.
Step 2
Combine sugar and lemon zest in a large bowl and rub them together until the sugar is fragrant and the lemon oils coat the sugar crystals. Add the eggs and whisk until the sugar is dissolved a bit and smooth. Add melted butter, oil, vanilla, sour cream and milk and whisk to blend well.
Step 3
Sift flour, baking powder, baking soda and salt into a medium bowl.
Step 4
Add half of the flour mixture and start to fold it in gently. Mix in remaining flour until evenly combined. Do not over-mix.
Step 5
Spoon the batter into the prepared pan and spread it out evenly. For a nice split down the center of the loaf, run your spatula down the middle lengthwise. Bake for 45-55 minutes until a skewer comes out clean. Transfer pan to a rack to cool 10 minutes. Lift the cake out of the pan and let cool completely on the rack.
Step 6
For the icing, combine icing sugar, lemon juice, milk and salt in a medium bowl and whisk until smooth. It should be thick and opaque white, but still flowing. Resist adding too much more liquid because otherwise you won’t get a nice thick icing that sets up firm on the cake. If it is too runny, it will be just a glaze. Pour the icing over the loaf, spread it out to drip over the edges a bit and then let it set until the icing dries out. Slice and serve!