Add Port and sugar to a small saucepan and simmer over medium-high heat until thick and syrupy, about 10 minutes.
Line a clean baking sheet with parchment paper. Make as small a hole as possible in each fig. Roll cheese into marble-size balls and place into the cavity of figs. Press figs into pistachios and wrap each with one piece prosciutto. Place on parchment-lined baking sheet, seam side down, spreading them one inch apart.
Heat a grill pan over medium heat and grill prosciutto-wrapped figs until prosciutto is crisp and figs are heated through, 6 to 8 minutes.
To serve, drizzle with olive oil and Port wine reduction; garnish with remaining pistachios.