In a large bowl, mix together the flour, salt, nutmeg, and 1 tablespoon of the sugar until combined. Cut the butter into small pieces above the bowl, stopping to stir and coat the butter bits in the flour mixture every few minutes.
Pinch the mixture together with your fingertips until it resembles the texture of damp sand. Add the water, a tablespoon at a time, mixing it with a fork, until the dough just holds together when you squeeze a fistful of it in your hand. Pat it into a rough cicle shape, then cover and refrigerate for 30 minutes.
While the dough is chilling, you can make the fruit filling. In a medium sized bowl, toss together the apricots, 1/3 cup sugar, 1 tablespoon corn starch, the cinnamon, and the vanilla extract. Set aside. In a small bowl, toss together the rhubarb and the remaining 1/3 cup sugar and 1 tablespoon corn starch and set it aside.
Preheat the oven to 375 degrees Fahrenheit. Take the dough out of the refrigerator and place it on a lightly-floured work surface. Use a lightly floured rolling pin to roll it out into a circle until it's about 1/4-inch thick. Transfer the circle onto a baking sheet lined with parchment paper.
Arrange the rhubarb slices in a single layer, leaving 2 inches of empty space around the edge. Arrange the apricots in a single layer on top of the rhubarb slices, again leaving 2-inches of empty space around the border. Fold the edges of the dough over the filling to create a 2-inch crust edge, and press the folded edge firmly.
Brush the exposed crust with the whisked egg, sprinkle the galette with the remaining 2 tablespoons of sugar, and bake in the oven for 50-60 minutes, or until the crust is deeply golden and the filling is bubbling. If you find the crust is browning too quickly, tent the galette with tinfoil. Once done, remove from the oven and allow to cool for 30 minutes before drizzling the fruit center with maple syrup and slicing and serving.