Preheat the oven to 325 degrees F (165 degrees C). Spray an 8 ½x4 ½-inch loaf pan with non-stick spray.
Whisk together sugar, eggs, olive oil, 2 tablespoons lemon zest, ¼ cup lemon juice, and vanilla extract together in a large bowl until thoroughly combined.
Add in 1 cup flour, baking powder, and ½ teaspoon salt and mix until just combined.
Pour in buttermilk and mix until just combined.
Add in remaining 1 cup flour and mix until just combined.
Pour batter into the prepared pan and tap the pan on the counter a few times to remove large air bubbles.
Bake in the preheated oven until the top springs back lightly when touched, 60 to 65 minutes. A toothpick inserted near the center should come out clean.
Allow bread to cool in the pan for 30 minutes before removing to a wire rack to cool completely.
To make icing, whisk powdered sugar, 2 tablespoons lemon juice, cream, ¼ teaspoon zest, and 1 pinch salt together in a small bowl until smooth.
Pour icing over cooled bread and allow it to set before slicing.
