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Step 1
Make the cinnamon roll dough: Place the milk in a microwave-safe bowl and microwave in 10-second bursts until it’s just barely warm, 30 to 40 seconds. Pour the milk into the bowl of a stand mixer and add the yeast and 2 tablespoons (32 grams) of the granulated sugar. Whisk to dissolve the yeast and let sit for 10 minutes until foamy.
Step 2
Add the remaining granulated sugar, eggs, melted butter, and vanilla, and whisk until smooth, then add the flour and salt. Attach the dough hook to the mixer and mix on low speed until the flour has been mostly incorporated, scraping down the sides of the bowl halfway, 2 to 3 minutes. Increase the mixer speed to medium and mix until the dough pulls away from the sides of the bowl and is smooth, 5 to 6 minutes. (If your dough appears too dry, add 1 tablespoon of flour and continue mixing.) Transfer the dough onto a lightly floured surface and knead with your hands to form it into a smooth ball. Generously grease the sides of the mixer bowl with butter and add the dough back to it. Tightly cover the bowl in plastic wrap and let sit at room temperature until almost doubled in size, 1 to 11⁄2 hours depending on the temperature of your kitchen.
Step 3
While the cinnamon rolls are rising, start making the brown butter cream cheese frosting: In a small saucepan over medium heat, melt the butter. Continue cooking, stirring often to prevent the bottom from burning, until the butter foams then darkens in color slightly and is very fragrant, 3 to 4 minutes. Immediately transfer the butter into a medium heatproof bowl, then transfer into the freezer to cool until mostly resolidified, about 1 hour. (Make sure to use either a metal or tempered glass mixing bowl so temperature shock is not an issue.)
Step 4
Add the cooled brown butter, cream cheese, confectioners’ sugar, vanilla, and salt to a stand mixer fitted with a paddle attachment. Mix on low speed just until the confectioners’ sugar is mostly incorporated, then increase to medium-high and whip until fluffy, 2 to 3 minutes. Set aside.
Step 5
Make the filling: In a medium mixing bowl combine brown sugar, melted butter, cinnamon, ginger, allspice, and salt. Mix with a rubber spatula until combined. The mixture will have the texture of very wet sand. Set aside.
Step 6
Generously butter a Cast Iron Casserole Pan. Punch down the dough and transfer onto a lightly floured work surface. Roll into a 1⁄4-inch thick rectangle that’s about 16 by 9 inches. Sprinkle the filling over the top of the dough and gently press it in with your hands so it sticks. Roll the dough into a tight cylinder, pinching the seams closed so the filling stays inside. Slice the log into 12 equal pieces and arrange into a 4x3 grid in the prepared casserole dish. Loosely cover the top with plastic wrap and let sit at room temperature until nearly doubled in size, 30 to 45 minutes.
Step 7
Preheat the oven to 350°F and arrange a rack in the middle of the oven. Uncover the cinnamon rolls and bake until the tops are light golden brown, 23 to 27 minutes.
Step 8
Remove from the oven and let cool for 20 minutes.
Step 9
Frost the cinnamon rolls by dolloping about 1⁄4 cup of the frosting on top of each roll and using the back of a spoon to smooth it out.