Preheat your oven to 350°F (175°C)
Grease and line a loaf pan with parchment paper
In a bowl, whisk together flour, salt, and baking powder. Set aside
In a bowl, combine granulated sugar and lemon zest. Use your fingers to rub them together until the sugar feels slightly moist and fragrant
Add the softened butter and beat until light and fluffy (about 3–4 minutes)
Add the oil and mix until combined
Add the eggs and mix until the batter is smooth
Mix in the vanilla bean paste and milk
Add the lemon juice and mix everything together until well combined
Add the dry ingredients and mix on low speed until just combined. Do not overmix
Transfer the batter to the prepared loaf pan and smooth the top
Bake for 50–60 minutes, or until a toothpick inserted into the center comes out clean
If the top browns too quickly, tent loosely with foil during the final 10–15 minutes
Allow the loaf to cool in the pan for 10–15 minutes, then transfer to a wire rack to cool completely
In a small bowl, whisk together powdered sugar, lemon juice, and milk until smooth and pourable
Adjust consistency as needed. Stir in lemon zest if desired
Once the loaf is completely cool, drizzle the glaze evenly over the top
Allow the glaze to set before slicing
