Preheat oven to 425°F.
On lightly floured surface, roll out dough into ¼-inch thickness or 14-inch circle. Transfer dough onto large square of parchment paper. Place on baking sheet and refrigerate.
Place lavender in small heat-safe bowl. Pour ½ cup boiling water over lavender flowers and steep for 3 minutes. Strain tea through a fine sieve set over a bowl; discard lavender. Whisk in cornstarch to make a paste.
In large bowl, toss together peaches, sugar, lemon zest, and lavender paste to coat. Slide parchment and dough onto work surface. Spoon and spread peach mixture onto centre of dough, leaving a 4-inch border.
Brush egg on exposed rim of dough. Lift pastry up over filling to form a circle, folding and crimping around edge and leaving centre uncovered (see note #2) Brush pastry with egg wash. Slide onto baking sheet.
Bake for 15 minutes, turning once. Reduce heat to 350°F. Bake for an additional 40 minutes, rotating baking sheet once or twice to ensure even browning. Repeat brushing with egg wash for a crisp pastry and sprinkle with some granulated sugar, if desired.
To serve, let galette cool overnight. Reheat or serve at room temperature, with a dollop of whipped cream or ice cream.