Heat the milk in a microwave-safe cup or bowl for 50 seconds, or just until it's warm. Peel the clove of garlic and cut it into three pieces.
In a small or medium saucepan, melt the butter over medium-high heat. Add the flour, whisk to combine and continue whisking and cooking the flour mixture for a minute. Lower the heat if it bubbles too much.
Slowly add the warmed milk, a little at a time, whisking it in as you go. Add the garlic, salt and pepper. Use a wooden spoon to stir the sauce over medium-high heat for 3 minutes, or until it's thick and smooth. It's ready when you can push the spoon through it and see the bottom of the pan. Turn off the heat and remove the garlic.
Cut or tear the basil leaves into small pieces and stir them into the sauce.
If you're not going to use the béchamel immediately, place a layer of wax paper or plastic wrap on its surface, so a film doesn't form. The sauce can sit at room temperature for up to two hours, then it needs to be refrigerated. It can be refrigerated in a tightly sealed container for 3-4 days.
Notes
Adding Nutmeg:
We don't use nutmeg in our béchamel sauce, even though it's traditional. If you don't mind its flavor, you can add some. Start with ⅛ teaspoon and stir it in, then taste the sauce to see if you want to add more.
Reheating:
To reheat béchamel sauce by itself, place it in a pot on the stove over low heat. Whisk constantly to prevent lumps, until it's heated through. This will give you a smoother result than using the microwave.
Once the béchamel is used in lasagna, however, you can reheat the lasagna in the microwave with no problem.
Freezing:
You can freeze béchamel sauce for up to three months, but it will separate. Thaw it overnight in the refrigerator, then add it to a pot on the stove to reheat it. Whisk it constantly over low heat, and it should reconstitute.