Pit and slice peaches into uniform slices. Layer with cinnamon sticks and coat with vanilla extract. Add sugar if desired. Refrigerate for at least 8 hours to allow flavors to combine.
Preheat oven to 375.
Unroll pie crust and press into tart pan. Prick bottom with fork and bake for 10 minutes.
Coat pie crust with raspberry jam.
In a medium bowl, whisk egg and yolks, sugar, flour, and vanilla paste. Whisk in milk gradually.
Pour custard mixture into crust. Bake for 25 to 35 minutes.
Allow tart to cool for at least 20 minutes. Top with peaches in overlapping concentric circles.
Serve with whipped cream, preferably homemade.