Preheat the oven to 350 degrees F. Grease and flour 2 (8½ x 4¼ x 2½-inch) loaf pans. You may also line the bottom with parchment paper, if desired.
Cream the 1 cup (8 ounces, 2 sticks) unsalted butter and 2 cups granulated sugar in the bowl of an electric mixer fitted with the paddle attachment, until light and fluffy, about 5 minutes. With the mixer on medium speed, add the 4 large eggs, 1 at a time, and the 1/3 cup grated lemon zest.
In a separate bowl, sift together the 3 cups all-purpose flour, 1/2 teaspoon baking powder, 1/2 teaspoon baking soda, and 1 teaspoon salt. In another bowl, combine 1/4 cup freshly squeezed lemon juice, 3/4 cup buttermilk, and 1 teaspoon lemon extract. Add the flour and buttermilk mixtures alternately to the batter, stirring as you go, beginning and ending with the flour.
Divide the batter evenly between the pans, smooth the tops, and bake for 45 minutes to 1 hour, until a cake tester comes out clean. Mine took 50 minutes to completely cook.
When the cakes are done, allow them to cool for 10-20 minutes. Remove the cakes from the pans and set them on a rack set over a tray or sheet pan.
For the glaze, combine 2 cups confectioners' sugar and 3 1/2 tablespoons freshly squeezed lemon juice in a bowl, mixing well until smooth. While cakes are still slightly warm, pour glaze over the tops of the cakes and allow the glaze to drizzle down the sides. Let cakes cool completely before slicing.
Cover and store leftover cake at room temperature for up to 3 days or up to 1 week in the refrigerator.