Preheat oven to 350°F (175°C). Grease and flour a 9-inch round cake pan, or line the bottom with parchment paper. Set aside.

In a medium bowl, whisk together the sifted all-purpose flour, baking powder, and salt. Set aside.

In a large mixing bowl, cream together the softened unsalted butter and 1 3/4 cups granulated sugar with an electric mixer on medium-high speed until light and fluffy, about 3-5 minutes.

Add the eggs one at a time, beating well after each addition until fully incorporated. Scrape down the sides of the bowl as needed.

In a separate small bowl, combine the buttermilk, 1/4 cup fresh lemon juice (for cake batter), 2 tablespoons lemon zest (for cake batter), and vanilla extract.

Gradually add the dry ingredients to the wet ingredients, alternating with the buttermilk mixture, beginning and ending with the dry ingredients. Mix on low speed until just combined. Be careful not to overmix, as this can lead to a tough cake.

Pour the batter evenly into the prepared cake pan.

Bake for 30-35 minutes, or until a wooden skewer inserted into the center of the cake comes out clean. The cake should be golden brown and spring back slightly when lightly pressed.

While the cake is baking, prepare the lemon syrup. In a small saucepan, combine 1/4 cup fresh lemon juice (for syrup) and 1/4 cup granulated sugar (for syrup). Heat over medium-low heat, stirring constantly until the sugar is fully dissolved. Remove from heat.

Once the cake is out of the oven, immediately poke numerous holes all over the top of the warm cake using a wooden skewer or fork. Slowly pour the warm lemon syrup evenly over the entire top surface of the cake, ensuring it soaks in.

Let the cake cool in the pan for 15-20 minutes before carefully inverting it onto a wire cooling rack to cool completely. Ensure the cake is fully cool before glazing.

Once the cake is completely cool, prepare the lemon glaze. In a small bowl, whisk together the sifted powdered sugar, 3-4 tablespoons of fresh lemon juice (for glaze - add one tablespoon at a time until desired consistency is reached), and optional 1 teaspoon lemon zest (for glaze). The glaze should be thick enough to coat the back of a spoon but still pourable. Adjust lemon juice as needed.

Drizzle or spread the lemon glaze evenly over the cooled cake. Allow the glaze to set for about 15-30 minutes before slicing and serving. Garnish with extra lemon zest if desired.