Heat the milk in a large measuring glass in the microwave for 1–2 minutes until just warmed through.
Melt the butter into the cooked leeks. Once bubbly, add the minced sage and cook for 45 seconds. Return the cooked mushrooms to the pot and season with salt. Add the roasted garlic paste and toss to combine.
Sprinkle the flour over the mushrooms and cook, stirring often, for 2–3 minutes. Next, add sweet vermouth and constantly stir to create a slurry.
Next, add the warm milk in 1 cup increments. Whisk after each addition until you have a smooth, creamy sauce. Next, add the nutmeg and then season to taste with salt and pepper. Finally, simmer the mushroom béchamel for 10–20 minutes until thickened.