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Gather your ingredients.
In a heavy-bottomed saucepan, melt 3 tablespoons of the butter over medium-low heat.
Stir in the flour to form a roux . Cook for 2 to 3 minutes, stirring frequently, until most of the water has cooked out (it will bubble less), which also allows the raw flour taste to cook off.
Slowly add 2 ½ cups of the warm milk while whisking or stirring constantly so that the liquid is incorporated into the roux without forming lumps.
Stick the cloves into the onion and add to the sauce along with the bay leaf. Simmer for about 10 minutes, or until it's reduced by about 20 percent.
Remove the bay leaf and the onion and strain the sauce through a fine-mesh strainer or a colander lined with cheesecloth. Make sure you retrieve all of the cloves.
Return the sauce to the pan. Add the Gruyère and Parmesan cheeses and stir until the cheese has melted.
Remove from heat, stir in the remaining 1 tablespoon butter, and adjust the consistency with some or all of the remaining ½ cup milk if necessary. Serve right away with pasta, chicken, or fish. Enjoy!