Preheat oven to 425°F. Place flour, salt, and 1 Tbsp sugar into bowl. Add butter, cut into small pieces, breaking up into flour with fingers until it's size of small peas. Add iced water and gently mix until it comes together. Place dough in ziplock bag and keep in fridge at least 30 minutes to relax.
In separate bowl, add blackberries, diced pear, 1 Tbsp sugar, and balsamic. Toss until blackberries and pears are coated. Roll dough out into 10" diameter circle. Transfer pastry carefully to large baking tray covered with parchment paper. Place blackberry pear mixture in a pile in center of pastry, leaving 2" border. Fold border in towards fruit creating a wall to stop filling from coming out. Using pastry brush, glaze pastry with milk and sprinkle with remaining Tbsp sugar.
Bake in oven 20 minutes. Reduce heat to 375°F. Bake an additional 40-45 minutes or until galette crust is golden and fruit is slightly bubbling. Let cool 10 minutes before slicing.