Prepare the oven and loaf pan: Preheat the oven to 350°F. Lightly grease a 9x5-inch loaf pan, then line it with parchment paper, leaving enough overhang along the sides to help lift out the baked loaf.
Combine the dry ingredients: Whisk together the flour, baking powder, baking soda, salt, and poppy seeds in a medium bowl. Set aside.
Make the lemon sugar: Add the granulated sugar and lemon zest directly to the bowl of a stand mixer. Rub the zest into the sugar with your fingertips until the mixture is fragrant and the sugar looks slightly moistened.
Cream the butter and lemon sugar: Add the softened butter to the lemon sugar and beat for 2-3 minutes, or until light and fluffy.
Add the eggs: With the mixer running on low to medium speed, add the eggs one at a time, mixing after each addition.
Mix in the remaining wet ingredients: Add the fresh lemon juice, oil, and vanilla extract and mix until incorporated. Add the sour cream and mix until combined.
Add the dry ingredients: Add the flour mixture in three additions, mixing on low speed just until incorporated after each addition. Avoid overmixing the batter.
Fill the loaf pan: Transfer the batter to the prepared pan and spread it into an even layer, smoothing the top.
Bake: Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean. If the top is browning too quickly, loosely tent the loaf with aluminum foil during the final 15 minutes of baking.
Cool: Let the bread cool in the pan for 10 minutes. Carefully lift it from the pan and transfer it to a wire rack to cool completely before glazing.
Make the lemon glaze: Whisk the powdered sugar with 2 tablespoons of fresh lemon juice until smooth. Add additional lemon juice as needed until the glaze reaches your preferred consistency.
Glaze and serve: Spoon or drizzle the glaze over the completely cooled loaf. If desired, garnish with thin lemon slices and fresh mint before slicing and serving.