Preheat oven to 375ºF, and grease/butter a 10-inch square baking dish.

Stir the milk and lemon juice (or vinegar) together in a bowl; allow to sit for 5 minutes.

In a large bowl, whisk the flour, sugar, baking powder, baking soda, and salt together. Pour the milk solution, melted butter, and vanilla into the middle of the dry ingredients. Stir together until dough just comes together; do not overmix. Knead with your hands until the dough forms into a ball. If dough is still too sticky to handle, add a little flour.

On a lightly-floured surface, roll dough out into a 13"x16" rectangle. Using a butter knife, spread softened butter evenly over the dough. Sprinkle the brown sugar over it, followed by the cinnamon. Lightly pat it down with your fingertips to help sugar adhere to dough. Roll dough tightly into a log, ending with the seam side down. Pinch the ends to seal.

Using plain, unwaxed dental floss (or a bench scraper), slice the log into 9 evenly-sized rolls. Arrange the rolls cut-side down in the prepared baking dish. Bake for 15-20 minutes, or until lightly golden on the surface, with melty, bubbly filling.

While rolls bake, prepare the frosting.

In a medium saucepan, melt the butter over medium-low heat. As the butter melts, it’ll start to foam, then turn a clear golden color. Continue to stir the butter, scraping up any browned specks from the bottom of the pan as it starts to brown. It should have a nutty aroma.

Once browned and nutty, turn off the heat and pour into a shallow bowl. Chill in the freezer until solid, about 10-15 minutes.

In the bowl of an electric stand mixer fitted with a paddle attachment, beat the brown butter and cream cheese together on high for about 1 minute. Add the vanilla, salt, and powdered sugar and beat for 2 minutes. Scrape down sides of the bowl, and beat on high for 1 more minute until light and fluffy.

Once rolls have baked, remove from the oven and immediately spread the frosting over the warm rolls. The frosting will melt into every crevice, moistening the rolls even more. Serve immediately.