Position the broiler rack 6" from the heat source and preheat the broiler. Line a large baking sheet with aluminum foil.
In a small bowl, mix sugar and spices. One at a time, dip figs, cut side down, in sugar mixture to coat. Then coat the figs a second time with the sugar mixture and arrange them cut side up on the baking sheet.
Broil figs, watching closely, for about 4 minutes, or until sugar melts and begins to caramelize and figs soften slightly and begin to ooze their juice.
Divide figs among 4 bowls. Spoon 1/3 cup of vanilla ice cream into each bowl and sprinkle with hazelnuts.