Combine 1 1/4 cups sugar and butter in a 9-inch cast-iron skillet. Cook over medium heat, stirring constantly, until sugar dissolves and butter melts, and mixture becomes golden brown in color. Set aside.
Combine remaining 2 1/2 cups sugar and 1 1/4 cups milk in a Dutch oven, stirring well. Bring to a boil; stir in reserved sugar mixture. Cook over medium high heat, stirring occasionally, until mixture reaches 230° (thread stage).
Remove from heat; cool slightly. Beat mixture at medium speed of electric mixer until spreading consistency. Stir in additional milk, if necessary, to maintain spreading consistency.