Place figs into a 9-inch (23cm) square baking dish, cut side up. Add rosemary and drizzle with honey and 1 tablespoon (15ml) olive oil. Season with salt and pepper. Roast until figs are softened and beginning to brown, 15 to 20 minutes. Set aside to cool slightly.
Set oven to broil and place the baguette slices on a baking sheet and drizzle with remaining olive oil. Season with salt. Broil until lightly toasted, 2 to 3 minutes, flipping halfway.
To serve, arrange toasts on a serving platter. Top with arugula, figs and cheese. Drizzle with more olive oil and sprinkle with salt and pepper, if desired.