In a 10.25-inch, fire-safe skillet, over medium high heat, combine the cornstarch, sugar, almond extract, orange juice, and cherries. Stir together until sugar dissolves, about 3-5 minutes, then continue to let the mixture simmer for another 5 minutes.
Pour the rum over the top of the cherries. Take a lighter and carefully light a fire on top of the rum. Gently shake the pan until the fire goes out, about 30 seconds.
Portion the ice cream into 4 bowls, then drizzle the cherries and juice over top. Serve immediately.
Use extreme caution when igniting alcohol. Remove the pan from the heat source before adding the alcohol. Pour the alcohol into the pan and carefully ignite with a match or click lighter. Return the pan to the heat and gently swirl to reduce the flames.