Start by peeling the onions. Slice them thinly using a sharp knife. Thin slices cook faster and become soft easily. Try to keep the slices even. This helps them cook at the same speed. Set them aside for cooking.

Place a saucepan on medium heat. Add butter and olive oil together. Let the butter melt slowly. Mixing oil with butter prevents burning. It also adds a nice flavor. Keep the heat gentle so the butter stays smooth.

Add the sliced onions to the pan. Stir them well so they are coated in butter. Cook on low heat for about 10 minutes. Stir often to avoid sticking. The onions should turn soft and slightly golden.

Sprinkle the flour over the cooked onions. Stir quickly using a wooden spoon. This forms a smooth paste. Cook for 1 to 2 minutes to remove the raw taste. Do not let it burn or turn too dark.

Slowly add warm milk to the pan. Pour a little at a time while stirring. This helps avoid lumps. Use a whisk if needed. Keep stirring until the sauce becomes smooth and creamy.

Add salt and black pepper to taste. Stir well to mix everything. You can also add a little mustard for extra flavor. A pinch of nutmeg gives a warm touch. These small additions make a big difference.

Let the sauce simmer on low heat for 5 to 7 minutes. Stir occasionally so it does not stick. The sauce will become thicker and richer. If it feels too thick, add a splash of milk.

Turn off the heat and let the sauce rest for a minute. Serve it warm over your favorite dish. It tastes best fresh and hot. Enjoy the creamy texture and mild onion flavor.