In a saucepan, saute onion in butter until translucent. Add mushrooms, garlic, soy sauce, salt & thyme. Cover & simmer on low for 10 minutes. Remove from heat; add heavy cream & cheese. Allow to cool.
In a bowl, combine beef with kalbi sauce; mix well.
Preheat oven to 350 F.
On a piece of plastic wrap, press out meat in a rectangle about a 1/4-inch thickness. Sprinkle meat with green onions. Top with mushroom filling. Using the plastic wrap, roll from the short end in a jelly-roll style.
On a piece of parchment paper, spread crushed french onions in a rectangle shape. Place meat roll on top & roll to cover it with the crushed french fried onions.
Place parchment paper with meat roll on a baking sheet & bake for about 50 minutes.