To make the fresh peach filling, whisk together the cornstarch and sugar in a medium saucepan. Toss the diced peaches in the fresh lemon juice and add to the saucepan along with the water. Cook over medium heat, whisking frequently. Cook until the mixture thickens and begins to bubble. Set aside to cool.
To make the bars, preheat the oven to 350 F. Cream the butter and sugar together in a large bowl. Beat in eggs and vanilla. In a separate bowl, whisk together the flour, baking powder and salt. Add the dry ingredients to the wet and stir until combined.
Grease a 10 x 15 inch baking pan. Reserve 1½ cup of batter, spread the rest on the bottom of the greased baking pan. Spread with the fresh peach filling. Using a teaspoon, dollop on the reserved batter in drops. Bake in preheated oven for 35 minutes or until lightly browned and toothpick inserted in the middle comes out clean. Do not over bake.
Let cool. To make the glaze, beat the powdered sugar, vanilla extract and enough milk to form a smooth consistency. Drizzle on cooled bars. Cut and serve. These are better the second day as the batter absorbs some of the moisture from the filling.
*1 (20 ounce) can of peach pie filling may be used instead of the fresh peach filling.