Peach-Tarragon Shortcake

Peaches Using the tip of a paring knife, score an X in the bottom of each peach. Cook in a large pot of boiling water just until skins begin to peel back where cut, about 1 minute. Using a slotted spoon, transfer to a bowl of ice water; let cool. Peel; cut over a medium bowl into 1/4"-thick wedges, collecting juices.
Add tarragon and sugar to peaches and toss to combine. Let stand, tossing occasionally, until peaches release their juices and sugar is dissolved, about 1 hour.
Preheat oven to 425°. Heat butter and tarragon in a small saucepan over medium heat until butter is melted; set aside.
Whisk cake flour, baking powder, salt, 1 cup all-purpose flour, and 2 teaspoons sugar in a large bowl. Drizzle chilled cream over and mix gently until dough holds together.
Turn out dough onto a lightly floured surface and knead into a shaggy ball, being careful not to overwork. Place on a parchment-lined rimmed baking sheet and form into an 8"-diameter disk, about 1/2" thick. Brush with some reserved melted butter and sprinkle with sugar.
Bake until shortcake edges are golden brown, 12–15 minutes. Reduce oven temperature to 325°. Bake until golden brown all over, 8–10 minutes longer.
Brush shortcake with remaining melted butter. Transfer to a wire rack and let cool. Cut shortcake into 8 wedges, spoon peaches and their juices over, and top with whipped cream.