Directions

1. Place grated cheese in a medium bowl and toss with cornstarch until evenly coated. Set aside.

2. Melt butter in a heavy medium saucepan or Dutch oven over medium-high heat. Add chopped onions and cook, stirring frequently, until the onions turn golden-brown (about 5 minutes).

3. Add 2 Tbsp of broth and deglaze the pan using a wooden spoon or spatula. Continue to cook, stirring frequently, until broth has largely evaporated and an oniony brown sauce has built up (approximately 2 more minutes).

4. Add another 2 Tbsp. broth and scrape up browned bits. Repeat cooking, adding a little broth, deglazing and scraping until onions have completely softened and have turned a deep, dark brown color (20-30 minutes total). Transfer to a small bowl.

5. Pour evaporated milk and Worcestershire sauce in the now empty saucepan. Whisk to combine as you bring to a boil over medium-high heat, scraping the bottom of the pan with a wooden spoon or spatula to release any remaining browned bits. Reduce heat to low and add the grated cheeses. Stir mixture constantly until cheese is melted and smooth. Add the caramelized onions and cognac, then sprinkle in the thyme.

6. Season with salt and pepper to taste. Transfer to a bowl and serve immediately.