To begin, coat the inside of your Bundt cake pan well with baking spray replacement, (or thoroughly coat it with butter and then sugar.) Set it aside for now.
Preheat your oven to 325° (F).
In a bowl, combine 2 3/4 cups of the flour, the baking powder and salt. Stir together and set aside for now.
In your mixing bowl, beat the sugar until it is light and fluffy.
Add the butter and beat until creamy.
Add the eggs, one at a time, mixing each in completely before adding the next.
Stir in the vanilla extract.
Add half of the flour mixture, mixing well before adding the second half. Again, mix it in well, but do not overmix it.
Place the diced, fresh peaches in a bowl and sprinkle with the remaining 1/4 cup of all purpose flour. Stir to coat.
Fold the peaches into the cake batter.
Spoon the thick batter into the prepared pan and smooth the top of the batter with the back of your spoon or spatula.
Bake for 60-70 minutes or until the cake tests done with a wooden pick.
When the cake is done, place the cake (still in the pan) on the cooling rack and let the cake cool for 10 minutes. Then invert the pan and cake onto the rack and let it sit there for at least 10 more minutes before you try to gently lift off the pan. If it sticks at all, simply let it sit for another 10 minutes before removing the pan. Allow the cake to fully cool.
When the cake is cool, prepare the glaze.
How to make the Brown Sugar Glaze
Combine the sugars, butter and half & half in a saucepan over medium high heat. Stir continually until the mixture boils. Let it boil hard for a full minute. The mixture should look almost glassy and frothy - more bubbles than anything.
After it has boiled hard, add the vanilla extract while stirring rapidly. The mixture will boil up when you add it. Stir and cook for about 30 more seconds then remove it from the heat.
Allow the glaze to cool a bit. The closer it gets to room temperature, the thicker it will get. When it is thickened, but not all the way cool, drizzle the glaze all over the top of the cake.