Preheat oven to 350° F.
In a large bowl, toss together sliced apples, cinnamon, nutmeg, sugar, and flour. Add rum and stir to combine. Pour the apple mixture into a 9x13 inch baking dish.
In a medium bowl, mix together flour, brown sugar, rolled oats, cinnamon, and nutmeg. Add melted butter and stir to combine until crumbly. Pour streusel topping over apple mixture. Bake uncovered for 50-60 minutes or until bubbly and apples are tender.
While apple crisp is baking, you can make the rum caramel. Heat the granulated sugar in a small saucepan over medium heat, stirring constantly just until the sugar is melted into a thick brown liquid, about 5-7 minutes. Once the sugar is completely melted, add the butter; bubbling will occur. Using a whisk, whisk until melted and slightly combined, about 1 minute. Next, slowly add the heavy whipping cream, whisking constantly; more bubbling will occur. Let the caramel boil for 30 seconds to 1 minute until it rises in the pan. Quickly whisk in rum, and remove from heat.
Once apple crisp is done, drizzle half of the rum caramel over the apple crisp in the pan. Pour remaining rum caramel into a small jar for drizzling over individual servings.