Heat the oven to 375F.
Divide the chilled dough into two discs. Wrap up the second disc and use for something else. (the dough freezes very well, when tightly wrapped)
Roll out the dough so that it's about an inch larger on all sides than a 9inch tart pan. Drape the dough over the pan and gently press down into the edges. Line the dough with parchment paper. Fill the parchment lined tart with baking beans (any dried beans or rice will work for this) and Par bake the crust for about 15 minutes. Remove from the oven, and carefully scoop out the beans, and remove the parchment.
While the crust par bakes, core and slice the peaches. The slices should be about a 1/2" thick.
Once your crust is par baked, add the frangipane to the crust and spread it out evenly.
Press the peach slices into the frangipane in a spiral, quite snugly together.
Bake for about 25 minutes. Remove from the oven and lightly brush the peach slices with simple syrup. Then continue to bake for 15-20 minutes, until the center is slightly puffed, the crust is golden brown, and the peaches are slightly caramelized.
Allow to cool in the pan for about 30 minutes before removing and cooling on a wire rack. Serve with ice cream. Yum!