Melt the butter in a pot over medium heat. Add the flour and stir until combined into a smooth mixture. Cook for about 2-3 minutes until the flour is slightly cooked, then remove from heat.

Gradually add the milk, half a cup at a time, stirring well each time before adding more. This will prevent lumps. Use a whisk to make mixing easier.

Continue adding milk until fully incorporated and smooth. Return to medium heat and stir continuously for about 5-7 minutes until the sauce thickens.