Preheat the oven to 350°F. Grease a 10-12 cup bundt pan by spraying evenly with nonstick baking spray, or spread softened butter all around the inside of the pan, and shake 1-2 Tbsp. flour around to coat, tapping out any excess flour.
In a small bowl, combine the brown sugar and cinnamon together. Set aside.
1 1/4 cup dark brown sugar, packed, 2 tsp. ground cinnamon
Open the cinnamon roll packages (reserve the frosting for later, place in the fridge) and separate the rolls. Cut each cinnamon roll in fourths and place them in a large bowl. Toss the 1-2 Tbsp. of the brown sugar cinnamon mixture into the rolls. Set aside.
3, (17.5 oz.) cans Pillsbury Cinnamon Rolls (Grands!)
Place diced apples in a medium-sized bowl. Mix 1-2 Tbsp. of the brown sugar cinnamon mixture into the apples and stir.
2 large granny smith apples, peeled and diced small
Place half of the apples down in the bundt pan first, followed by half of the cinnamon roll pieces. Add the remaining apples, followed by the rest of the cinnamon rolls, in an even layer.
Melt the butter in a microwave-safe bowl (cover with a paper towel so it doesn't splatter). Then, stir in the rum and the remaining brown sugar mixture. If the mixture seems too thin, add more brown sugar until it becomes a goopy consistency. Pour this on top all over the monkey bread.
Bake for ~45 minutes or until golden brown and no longer doughy in the middle. Remove from the oven and let cool for 10 minutes.
Carefully flip/invert the monkey bread onto a plate. Add the reserved frosting to a microwave-safe bowl and briefly microwave, just for 10-15 seconds. Drizzle on top of the bread once it has cooled down a bit (You don't have to drizzle on all of it, feel free to keep some on the side). Pull apart and enjoy!