How to Make It
Combine flour, 1 tablespoon sugar, and 1/2 teaspoon salt in bowl of a food processor. Pulse until well combined, about 5 times. Add cubed chilled butter; pulse until mixture resembles small peas, about 12 times. Add 1/4 cup ice water; pulse until mixture is evenly moistened, about 8 times. Mixture should hold together when pinched. If it doesn’t, add remaining 1 tablespoon ice water, 1 teaspoon at a time, pulsing 3 times after each addition. Turn mixture out onto a clean work surface. Shape into a ball, and flatten into a disk. Wrap tightly in plastic wrap. Chill at least 2 hours or up to 3 days.
Unwrap dough, and place on a lightly floured surface. Roll out into a 14-inch circle (about 1/8 inch thick). Trim into a 12-inch circle; discard scraps. Place dough circle on a parchment paper–lined rimmed baking sheet, and chill, uncovered, until firm, about 30 minutes.
Meanwhile, preheat oven to 425°F. Whisk together cornstarch, 1/3 cup sugar, and remaining 1/4 teaspoon salt in a large bowl. Add peaches, blackberries, melted butter, lemon zest and juice, and thyme sprigs; toss to combine.
Arrange fruit mixture in center of chilled dough circle, leaving a 1 1/2-inch border. Fold dough edges up and over filling (dough will only partially cover filling), pleating every 3 inches. Lightly brush folded dough edges with beaten egg. Sprinkle dough edges and filling with remaining 1 tablespoon sugar.
Bake in preheated oven 15 minutes. Reduce oven temperature to 350°F (without opening oven door), and bake until crust is golden brown and fruit mixture bubbles in middle, 40 to 45 minutes.
Transfer baking sheet with galette to a wire rack, and let cool 30 minutes. Microwave jelly in a small microwavable bowl until melted, 30 to 45 seconds, stirring every 15 seconds. Brush jelly over warm fruit filling. Serve galette warm, or let cool completely to room temperature, about 1 hour.