Preheat the oven to 350F degrees; butter a 10-inch spring form pan or similar.
Sift together the flour, baking powder, and salt into a small bowl. In another bowl, whisk together the plain yogurt, ¾ cup sugar, eggs, lemon extract and juice, vanilla extract and oil.
Slowly whisk the dry ingredients into the wet ingredients, mixing just until evenly mixed but taking care not to over mix. Pour the batter into the prepared pan and bake for 28-30 minutes, or until a cake tester placed in the center of the cake comes out clean.
While the cake is baking, cook the 4 tablespoons lemon juice and remaining 4 tablespoons sugar in a small pan until the sugar dissolves and the mixture is clear.
When the cake is done, allow it to cool in the pan for 10 minutes on a cooling rack. Carefully remove cake from pan and place on cooling rack. While the cake is still warm, pour the lemon-sugar mixture over the cake and allow it to soak in. Cool completely.
While the cake cools, make the glaze by combining powdered sugar, melted butter, meyer lemon juice, pinch of salt and half & half. Mix to combine. Adjust ingredients if glaze is too thick add a tablespoon or two of powdered sugar at a time or lemon juice to thin. Pour the glaze evenly over the completely cooled cake.
If desired, garnish with meyer lemon zest and/or sliced meyer lemons.
