Line a baking sheet with parchment or a silicone baking mat and set aside.
In a large skillet over low heat, melt 1 tablespoon of the butter with the olive oil. Add the onions and stir to coat. Cook the onions, stirring occasionally, until they’re deep brown and fragrant, about 25 minutes. Set aside to cool.
While the onions are cooling, in a large mixing bowl, whisk together both flours, baking powder, baking soda, salt, and sugar until just combined.
Slice the remaining 8 tablespoons of butter into small cubes and scatter over the top of the flour mixture. Using your fingertips and working quickly, rub the butter into the flour mixture until it resembles small, coarse peas.
In a separate small bowl, whisk together the buttermilk and large egg. Add the liquid ingredients to the dry ingredients and stir until the dough comes together. Fold in the figs, Parmesan, caramelized onions and thyme.
Scrape dough onto a clean, well-floured counter top and pat into a 7-inch circle about 1 inch thick.
In a small bowl, whisk 1 teaspoon water with the egg yolk and brush the egg wash over the top of the dough circle. Slice into 6 even wedges (or, for smaller scones, 8). Lay each wedge onto the prepared baking sheet.
Place the baking sheet in the freezer for 30 minutes. Meanwhile, preheat the oven to 375°F.
Bake scones for 30 minutes or until they’re golden brown on top and around the edges. Transfer to a wire rack to cool.