Melt butter in a large saucepan over medium heat. Whisk in flour until combined. Slowly add 1 cup of hot milk and whisk until the mixture is smooth. Repeat with remaining milk, adding it gradually and stirring until smooth after each addition. Once all the milk has been added, bring to a gentle simmer to ensure flour has thickened to its capacity. Continue to cook for 5-10 minutes, stirring occasionally.