In a small bowl, combine the warm milk, yeast, and 1 tablespoon of the sugar. Let sit for 5–10 minutes, until foamy.
In a large mixing bowl, whisk together the remaining sugar, egg, egg yolk, and melted butter. Add the yeast mixture and stir to combine.
Gradually add the flour and salt, mixing until a soft dough forms. Knead by hand for 8–10 minutes, or in a stand mixer fitted with a dough hook for 5–7 minutes, until the dough is smooth, elastic, and slightly tacky.
If the dough is very sticky, add flour one tablespoon at a time, being careful not to add too much.
Transfer the dough to a lightly greased bowl and cover with a clean kitchen towel or plastic wrap. Let rise in a warm, draft-free place for 1–1½ hours, or until doubled in size.
In a small bowl, combine the softened butter, brown sugar, cinnamon, and salt. Mix until a thick, spreadable paste forms.
The salt is important here. It balances the sweetness of the brown sugar and brings out the warmth of the cinnamon without making the filling taste salty.
Turn the risen dough onto a lightly floured surface. Roll into a rectangle approximately 14 × 10 inches.
Spread the cinnamon filling evenly over the dough, leaving about ½ inch uncovered along one long edge.
Starting from the opposite long edge, roll the dough tightly into a log. Pinch the seam closed.
Using a sharp knife or unflavored dental floss, cut into 7–8 equal rolls.
Lightly butter the Lancaster No. 8 Skillet and arrange the cinnamon buns inside, leaving a little room between each one for expansion.
Cover the skillet loosely and let the buns rise for another 30–45 minutes, or until noticeably puffy and nearly doubled.
They should look soft and fill out the skillet, but they don't need to be completely touching.
Preheat the oven to 350°F.
Once the buns have finished their second rise, gently drizzle the warmed heavy cream evenly over the tops and in between the rolls.
Transfer the skillet to the oven and bake for 25–30 minutes, until the tops are lightly golden brown and the centers are cooked through. If the tops brown too quickly, loosely tent with foil for the remaining baking time.
Let cool for about 10 minutes before glazing.
In a medium bowl, beat the softened cream cheese and butter until smooth and creamy.
Add the powdered sugar, vanilla, and a pinch of salt. Beat until combined.
Add the milk or heavy cream one tablespoon at a time until the glaze reaches your preferred consistency. It should be thick but easily spreadable.
Spread the glaze generously over the warm cinnamon buns, allowing it to melt into the swirls.
Serve warm, straight from the Lancaster No. 8 Skillet.
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