For the rolls:
⅔ cup whole milk
1 ¾ teaspoons instant, quick rise, or bread machine yeast
3 tablespoons granulated sugar
1 egg, lightly beaten
3 tablespoons unsalted butter, melted
3 cups flour, plus more as needed
¾ teaspoon fine sea salt
For the brown sugar sprinkle:
½ cup (packed) dark brown sugar
1 tablespoon ground cinnamon
¼ teaspoon grated nutmeg
¼ teaspoon fine sea salt
For the banana filling:
3 medium firm, ripe bananas, diced
1 tablespoon bourbon
1 stick (8 tablespoons) unsalted butter, at room temperature
3 tablespoons granulated sugar
For the frosting:
6 tablespoons (3 ounces) cream cheese, at room temperature
1 cup confectioners’ sugar
¼ teaspoon salt
1 tablespoon whole milk
1 tablespoon bourbon
Make the bun dough:
Place the milk in a microwave-safe mug and microwave on high until warm (about 110°F), 30–35 seconds. (Use a thermometer or your finger; it should feel like really warm bath water, but not scalding hot.) Add the milk to the bowl of a stand mixer and scatter the yeast on top, then add the sugar, egg, and melted butter.
Attach the dough hook, and mix on low speed until the ingredients begin to unify, 15 seconds. Increase the speed to medium-low, gradually add the flour, and mix the dough for 3 minutes, then add the salt. Continue to mix until the dough is slightly tacky but pulls away from the sides and bottom of the mixer, about 5 minutes. Lightly grease a medium bowl, transfer the dough to the bowl, seal with plastic wrap, and let rise in a warm place until doubled in size, 1 hour 15 minutes.
While the dough is rising, make the brown sugar sprinkle:
In a small bowl, combine the brown sugar, 2 teaspoons of the cinnamon, the nutmeg, and ⅛ teaspoon salt.
Make the banana filling:
Heat 5 tablespoons of the butter in a 9- or 10-inch skillet over medium-high heat, stirring often, until foamy and toasty with brown flecks, 4 minutes. Scoop out 2 tablespoons of the brown butter and place in a small heatproof bowl, then set aside for the frosting.
To the skillet, add the bananas, sugar, bourbon, remaining teaspoon cinnamon, and remaining ⅛ teaspoon salt and cook, shaking and stirring occasionally, until the liquid begins to thicken, 3–4 minutes. Transfer the banana mixture to a plate to cool to room temperature.
Fill and form the rolls:
Line the bottom and sides of a 13x9 baking pan large cast iron skillet with parchment paper. Once the dough has risen, lightly flour a work surface and turn the dough out onto the surface.
Gently shape the dough into a rectangle, then roll out into a 9x14-inch rectangle. Spread the remaining 3 tablespoons of room temperature butter over the dough, then sprinkle and press the brown sugar mixture into the butter. Spoon the banana mixture evenly over the sugar, pressing gently. Starting from one of the short ends, roll the dough into a tight log, trying to pull the sides of the dough out as you go to keep the roll uniform.
Trim ½ inch off each end, then use a ruler to mark the roll evenly into 12 pieces (each about 1 inch thick). Dust a serrated knife with a little flour and gently saw through the dough to create 9 rolls. Carefully separate the rolls (some filling might try to escape, keep it in line!) and fit them into the pan. Seal with plastic wrap and let rise again until puffy, about 45 minutes.
Preheat the oven to 350°F. Remove the plastic wrap and bake the rolls until fluffy and golden on top, about 25 minutes.
While the rolls are baking, make the frosting:
In the bowl of an electric mixer fitted with the paddle attachment, combine the cream cheese, reserved 2 tablespoons brown butter, confectioners’ sugar, and salt and beat on low speed for 30 seconds. Increase the speed to high, beat 30 seconds, then add the milk and bourbon and beat until fluffy and light, 2–3 minutes.
Remove the rolls from the oven, let cool for 5 minutes, then spread the frosting on the rolls.
