Start by heating a heavy-bottomed saucepan over medium heat. Add 2 tablespoons of butter, letting it melt slowly. Once melted, sprinkle in 2 tablespoons of all-purpose flour. Stir it continuously for about two minutes, allowing the mixture to bubble but not brown. This roux serves as the foundation of your béchamel, so make sure to keep stirring!

While the roux is cooking, heat 4 cups of full-fat milk in a separate saucepan until it is warm, but not boiling. This step will help the sauce come together smoothly. Add in the halved onion, crushed garlic clove, bay leaf, and thyme. Let this simmer for about 10 minutes, allowing the flavors to meld.

Now comes the fun part. Gradually whisk the warm milk mixture into the roux, ensuring there are no lumps. Continue to stir until the sauce thickens, which should take around 5 to 10 minutes. As it cooks, you’ll witness the magic transform right before your eyes!

Once your sauce has thickened to your desired consistency, remove it from the heat. Take out the onion, garlic, bay leaf, and thyme sprigs. Now, season the béchamel sauce with a pinch of freshly grated nutmeg, coarse sea salt, and freshly ground white pepper. If you're feeling adventurous, mix in the Dijon mustard for that extra kick.

At this point, it's wise to taste your creation. Does it make your taste buds dance a little? If it's too thick for your liking, add a splash more milk. If you find it needs more seasoning, go right ahead and adjust as necessary!