In an 8-inch cast-iron skillet, combine the milk, water and salt. Place over medium-high heat and bring to a boil. Add 1 tablespoon of flour at a time, whisking constantly, until all of the flour has been added, about 5 minutes. Reduce the heat to medium and cook at a low simmer, stirring occasionally with a wooden spoon, until the muas has thickened and formed a skin, 12 to 15 minutes.
When the mixture has thickened, add the eggs to the pan, lightly mixing to incorporate. Continue to cook until the bottom sets, another 1 to 2 minutes, then remove from the heat. Taste and adjust the seasoning with salt. Drizzle with brown butter and top with cinnamon and sugar. Serve immediately.