Preheat the oven to 350°F. Grease and flour a 9x5-inch loaf pan.
In a large bowl, cream the softened butter, then add the sugar and beat until fluffy. Add the eggs one at a time, mixing well after each addition.
1 cup unsalted butter, 1 ¼ cups granulated sugar, 3 large eggs
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. In another bowl, mix the buttermilk and Greek yogurt.
2 cups all-purpose flour, ½ teaspoon baking powder, ¼ teaspoon baking soda, ¼ teaspoon salt, ½ cup buttermilk, ½ cup plain Greek yogurt
Gradually add the dry ingredients to the wet ingredients, alternating with the buttermilk mixture, starting and ending with the dry ingredients. Stir in the lemon zest, lemon juice, lemon extract, and vanilla.
zest of 2 lemons, ¼ cup fresh lemon juice, 1 teaspoon vanilla extract, 1 teaspoon lemon extract
Pour the batter into the loaf pan, smooth the top, and bake for 55-60 minutes, or until a toothpick comes out clean. Let the cake cool in the pan for 15 minutes, then transfer it to a wire rack to cool completely.
For the glaze, whisk together powdered sugar, lemon juice (start with 1 tablespoon), milk, and lemon extract until smooth. Adjust the thickness if needed by adding more powdered sugar or liquid.
1 cup powdered sugar, 1-2 tablespoons fresh lemon juice, 1 tablespoon milk, ½ teaspoon lemon extract
Once the cake is cool, drizzle the glaze over the top and let it set for 15-20 minutes. Slice and serve!