Pulse together flours, sugar, and salt in a food processor. Add butter and process until mixture is crumbly with some pea-sized pieces. Drizzle with water and lemon juice; pulse a few more times. Transfer dough to a large bowl; gently knead until it comes together. Wrap in plastic wrap and chill for 1 hour.

Unwrap dough; let stand for 5 to 10 minutes. Place on a floured piece of parchment paper and roll out into a 13-inch circle about 1/4-inch thick. Slide parchment with dough onto a baking sheet.

Stir mascarpone in a small bowl until softened. Stir in egg yolk, honey, and vanilla. Spread onto dough, leaving a 2-inch border. Arrange figs in concentric circles on top, alternating light and dark figs if using a mixture. Use parchment to help lift dough edges as you fold dough edges over fruit, pleating as necessary. Leave fruit exposed in the center. Chill, covered, for 1 hour.

Preheat the oven to 375 degrees F (190 degrees C).

Uncover and brush dough edges with milk. Sprinkle entire galette with turbinado sugar.

Bake in the preheated oven until crust is golden and filling is bubbly, 40 to 45 minutes. Transfer to a wire rack and let cool for 30 minutes.