Preheat the oven to 375 degrees F.
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.
Top each slice of toast with 2 teaspoons of fig jam, a slice of apple and a piece of shaved Pecorino Romano. Transfer the toasts to a serving platter and serve.
In a saucepan combine water and sugar over medium heat. Bring to a boil, reduce heat and simmer for 5 minutes, until the sugar has dissolved. Take pan off heat and cool the syrup. Any extra cooled syrup can be saved in an airtight container in the refrigerator.