Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease. Reduce heat to low.
Stir butter into cooked sausage until melted; whisk in flour. Cook, whisking constantly, until mixture is the color of peanut butter, 5 to 10 minutes. Season with 1 teaspoon salt and 30 grinds of black pepper.
Increase heat to medium and pour in 3 cups milk. Bring to a simmer, stirring constantly. Stir in remaining 3 cups milk, 1/4 cup at time, allowing mixture to return to a simmer after each addition, 10 to 15 minutes. Continue cooking and stirring until desired thickness is reached, 5 to 10 minutes. Season with 30 grinds of black pepper and salt to taste.
