Add 2 cups of peach chunks to a food processor and process until smooth. Set aside.
In a large bowl, using an electric hand mixer or stand mixer, mix together cream cheese, mascarpone cheese and 1 cup of sugar on medium-low speed until combined. Stop once to scrape the sides and bottom of the bowl. Do not mix on high speed or overmix, as the mascarpone cheese can begin to separate.
In a chilled mixing bowl, add the cold heavy whipping cream, remaining two tablespoons of sugar and vanilla extract. Whip on high speed until stiff peaks form. Manually, using a spatula, fold the whipped cream into the mascarpone cream cheese mixture.
Add the peach mixture to the gelatin mixture, mix.
Add the peach gelatin mixture to the cheesecake batter and mix to combine.
Fold in with a spatula the remaining 2 cups of peach chunks.
Spread the cheesecake filling evenly on top of the crust.
Set the cheesecake in the refrigerator to chill and firm, 5-6 hours or better, overnight.