Take cream cheese out of the refrigerator 30-45 minutes before cooking and defrost the sheet of puff pastry.
Slice peaches in half around the pit and separate in two. Take out the pit and slice each half into thin slices.
Take the pits out of apricots as well and take off the skin. Melt butter in a saucepot over medium-low heat and mix in brown sugar. Add apricots to the pot and mash them with a wooden spoon. Cover and let then cook until completely softened. Add Amaretto and let it simmer for a few minutes. Use an immersion blender to blend the apricot mixture until smooth. Set aside to cool down.
In a small bowl, blend together cream cheese, sugar, vanilla extract, and milk until smooth.
Preheat oven to 425 and grease a 9-inch round tart pan or a baking dish.
Gently roll out the puff pastry sheet a little bit, not too thin, and fit it into the prepared tart pan. Cut off the edges that are sticking out and fit them back around the sides.
Spread cream cheese mixture all over the bottom of the puff pastry but do it gently do you don’t push or rip the dough.
Spread apricot sauce over the cream cheese. Nestle the thin slices of peaches into the apricot sauce to create a rose petal pattern all over the top.
Bake for about 20-23 minutes, or until the pastry is deep golden brown.