Milk fudge is similar to dulce de leche, but in solid form. The fudge is rich with the flavor of caramelized sugar and browned butter.
Line an 8-inch square pan with buttered parchment paper or foil that extends over two sides. Bring to a boil in a large pot or Dutch oven over medium-high heat:
Watch carefully—the mixture has a tendency to boil over. Boil, stirring frequently. At about 10 minutes, the mixture will start to turn a light caramel color. At about 20 minutes it will be a deep caramel color. Continue to cook until the mixture reaches 240°F, 40 to 45 minutes total. Remove from the heat and stir in:
Discard the cinnamon stick. Transfer the mixture to a stand mixer or a bowl and beat on medium speed, using the paddle attachment, a handheld electric mixer, or a wooden spoon, until visibly thickened and no longer shiny but not hard or clumpy, 3 to 5 minutes. Transfer the fudge to the prepared pan. The mixture will be quite thick, so you may need to press it into the pan. Let stand for at least 1 hour. Remove the fudge from the pan and peel off the foil or parchment paper. Cut the fudge into 1-inch squares and store.