Preheat oven to 350ºF. Generously grease a 9-inch round cake pan with butter, oil or non-stick cooking spray.
Combine strawberries and 1 tablespoon sugar in a bowl, stir to coat berries and set aside.
Stir together flour, remaining 1 cup sugar, lemon zest, baking powder, baking soda and salt in a large mixing bowl. Stir together buttermilk, oil and eggs until blended. Make a well in the dry ingredients and pour in liquid mixture; stir gently but thoroughly until well mixed. Remove the strawberries with a spoon from the small bowl, reserving the liquid that collects in the bottom. Fold the strawberries into the batter until evenly incorporated.
Pour batter into prepared baking pan and bake in the center of the preheated oven until toothpick inserted in the center of the cake comes out clean, 42-50 minutes. Remove cake to wire rack and let cool slightly in pan until cool enough to handle, 15-20 minutes. Slide a sharp knife around the edge of the pan if cake is sticking. Invert cake onto wire rack and give a good tap to remove cake from pan. Cool cake completely.
To make glaze: stir reserved strawberry-sugar liquid (you should have about 1 tablespoon) and 2 teaspoons lemon juice into sifted powder sugar. Add more lemon juice to achieve desired consistency. Drizzle cake with glaze and decorate center with strawberries. Garnish with lemon zest if desired.
Makes 8 to 12 servings.