Gather all ingredients and equipment. Using a kitchen scale, scale all ingredients.
Combine 1/2 of the butter and half of the sugar, pureed peaches and lemon zest and bring to a boil, stirring gently.
Whisk yolks with the remaining sugar. Temper 1/3 of the hot mixture into the yolks and sugar mixture, while whisking. Then add this mixture back into the saucepan.
Continue cooking, stirring constantly with the whisk, until mixture comes to a boil. Whisk in the remaining butter.
Strain the thickened curd into a bowl using a fine mesh sieve. Place plastic wrap on top of the curd and refrigerate.
Preheat oven to 400 degrees. Place the pie crust into a 9 inch tart pan. Dock the dough with a fork. At this point you're going to blind bake the crust. Place parchment paper over the dough and fill the parchment paper with dried beans. (This will keep the pie crust from bubbling up) Bake for 15 minutes. Remove parchment and beans, lower heat to 350 and bake a few more minutes, or until pie crust is just turning golden.
Remove from oven and let cool.
In the meantime make the whipped cream. In a mixer beat the cream on high until it thickens into whipped cream. In a food processor, mix the confectioner's sugar and the fresh basil. Add the sugar mixture to the whipped cream and mix on low until blended. Taste and adjust flavors. Refrigerate until ready to use.
With a spatula spread the peach curd onto the tart. Garnish with fresh peach slices and a dollop of the Basil Sugar Whipped Cream.