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Place a small saucepan over medium heat. Add the figs, simple syrup, and brandy. Bring the mixture up to a simmer. Turn off the heat and let sit for 10 minutes. Place the fig mixture and the hazelnuts in a food processor and blend, pulsing a few times, until pureed. Set aside.
Place the baguette slices on a heavy baking sheet. Drizzle with olive oil. Top each slice with 1 teaspoon grated Pecorino Romano. Bake until the bread is toasted and the cheese is melted and golden, about 7 minutes.