Make dough: Combine flour, sugar, and salt in bowl of a stand mixer. Add butter. Using the paddle attachment, mix on low speed until butter is smaller than pea-size but not totally crumbly. Whisk egg yolk, cream, vanilla, and thyme in a small bowl and add to flour mixture. Blend just until dough comes together and is smooth. Do not overmix--otherwise it will be tough.
Form dough into a disk. Wrap in plastic wrap and chill at least 2 hours and up to 4 days.
Make custard: Heat milk and cream in a medium saucepan over medium-low heat until it begins to simmer. Add vanilla bean (pod and seeds) and let sit off the heat, covered, until flavor has developed, about 30 minutes.
Rewarm milk mixture over medium-high heat until almost simmering. Meanwhile, mix yolks and sugar in a medium bowl. Whisk in cornstarch and salt. Slowly whisk hot milk mixture into yolk mixture, 1/2 cup at a time. Pour mixture into same pan and cook, whisking constantly, until as thick as pudding, about 4 minutes. Pour custard through a strainer into a clean bowl (discard vanilla bean pod).
Lay a piece of plastic wrap over custard to prevent a skin from forming. Chill until cold, at least 3 hours and up to 4 days.
Form and bake tart shell: Preheat oven to 375°. Lightly grease a 6- to 7-in. tart pan with a removable side. Roll dough out on a lightly floured surface until about 1/4 in. thick or slightly thicker. Roll dough onto rolling pin, then unroll over pan. Press dough flush against bottom of pan, into bottom corners, and lastly up sides. Use your thumb to brush dough even with edge of pan. If you have any cracks or holes, patch with extra dough from the edges. You may have left over dough.
Lay a piece of parchment paper into pan over dough, cutting to fit as needed. Fill parchment with dried beans or pie weights.
Bake tart shell until edges are light golden brown, about 20 minutes. Carefully remove parchment with beans and transfer to a plate or a tray. Bake tart shell until center looks dry and is starting to turn golden brown, about 15 minutes more. Let cool completely. Remove tart from pan by setting on a can and letting side fall away. Carefully transfer tart, still resting on pan's bottom, to a large serving plate.
Assemble tart: Whisk cold custard to smoothen it. Spread or pipe cold custard into tart shell.
Heat butter in a medium frying pan over high heat. Add sugars and cook until they start to melt, about 20 seconds. Add peaches, remove from heat, and stir until juices are released and sugar has melted completely, about 1 minute.
Arrange peach wedges over surface of tart and pour warm peach juices over top. Sprinkle with fresh thyme.