Weigh or measure the sugar into a small bowl and set aside. Then, in another bowl, weigh or measure the flour.

Using a hand-held or stand mixer, blend the cream cheese and butter on medium speed for 2 to 3 minutes. Scrape down the bowl and add the sugar. Blend these for 2 minutes on medium speed. You want the mixture to be smooth-looking. This will tell you that the sugar has been incorporated. Scrape down the sides and turn the mixer back on at a low speed. Slowly add the flour. I usually scrape down the sides and across the bottom and turn the mixer on again for about another 30 seconds. Cover the mixer bowl and refrigerate for an hour.

While the cookie dough is in the refrigerator, take the skin off the white peach and take the pit out. Cut the peach into small pieces and add them to a small bowl. Sprinkle the sugar and the lemon juice over the cut-up peaches. Stir them around, so the pieces of peach get coated. Let them sit for about 5 minutes in the juice. After 5 minutes, drain them using a strainer and then lay them out on a paper towel. The goal is to get as much juice out of the peach pieces without smashing them. Change the paper towel that the peach pieces are laying on a couple of times; it will help draw the juice out.

Preheat the oven to 350°F (175°C or 180°C), and line 2 cookie sheet pans with parchment paper. For these cookies, I use a medium cookie scoop. Take the cookie dough scoop, make a ball using your hands, and place it on the cookie sheet. I get 12 balls to a sheet pan. Taking your thumb and pushing down right through the middle of the dough ball to make a well. I move my thumb around in a circular motion, so the well opens up some to accommodate more of the jam. Fill the well with the jam. I use a teaspoon to push the jam off the spoon; this is easier than using a measuring spoon.

Bake for 12 - 14 minutes until they are light brown on the bottom. Then, move the cookies to a cooling rack and let them cool completely. If you would like to add a little more peach flavor to your cookies, you can add a piece of the cut-up peach on the paper towel. Press lightly; the sticky preserves will hold the peach in place. Just make sure you have as much juice out of the peaches so there won't be a wet spot on the bottom of your cookies. Then sprinkle some powdered sugar on top to finish off the cookie.