Preheat oven to 375 degrees F.
Cut the top ¼ off the head of garlic. Drizzle 1 tablespoon of olive oil on the cut side. Wrap the garlic bulb in aluminum foil, and bake in the oven at 375 degrees F for 1 hour. After 1 hour, unwrap and allow to cool.
When garlic is almost done roasting, heat griddle on low to medium-low until it reaches about 350-375 degrees F. Set a skillet on the cooler side of the griddle.
While griddle is heating, prep the steak. Dry the steak with paper towels, and cut into ¾" - 1" cubes. To a medium bowl, add 2 tablespoons olive oil, 2 tablespoons Worcestershire sauce, 1 teaspoon thyme, and about ¼ of the roasted garlic. (The garlic should just squeeze out of the bulb in a paste-like consistency.) Add the cubed steak to the bowl and toss to combine. Season the steak lightly with salt and pepper and set to the side.
To the skillet on the griddle, add 2 tablespoons of butter and about ¾ of the roasted garlic. Mix the roasted garlic into the melted butter and cook for about 1-2 minutes. Then add 1 cup heavy cream, ¼ cup shredded Asiago, and ¼ cup crumbled gorgonzola. Stir to combine. Once the sauce is almost to a boil, move the skillet to the cooler side of the griddle and continue to cook, stirring occasionally until sauce has thickened.
While sauce is cooking, add about 1 tablespoon of cooking oil to the griddle surface and spread it around with your spatula. Add the mushrooms to the oiled surface and cook on the first side to develop a nice color. Then flip the mushrooms to the second side and cook an additional 1-2 minutes or until tender.
While mushrooms are cooking, add the diced shallots to the griddle and saute until tender. When mushrooms and shallots are done, combine them together and move to the cooler side of the griddle.
Add about 1 tablespoon of cooking oil and 1 tablespoon of butter to the hot zone on your griddle. Add the gnocchi to the butter/oil and toss to coat. Cook the gnocchi for about 1-2 minutes, then squirt water on the griddle near the gnocchi and cover with a melting dome to steam. Steam the gnocchi for about 1-2 minutes. Then uncover and continue to cook the gnocchi on the griddle, tossing occasionally, until lightly golden and done to your liking. Then move to the cooler side of the griddle.
Set up a sear zone on your griddle (about 450-475 degrees F). Add about 1 tablespoon of cooking oil to the griddle and spread it around with your spatula. Add the cubed steak to the oiled surface so that each piece is in contact with the griddle top. Cook on the first side until a nice color develops (about 2-3 minutes). Then flip to the next side and continue to cook until steak is done to your liking. Add the cooked mushrooms and shallots to the steak.
Finish the dish - Add the toasted gnocchi to the skillet with the garlic cream sauce and toss to combine. Lay the steak bites on top of the gnocchi. Garnish with a sprinkling of cheese or fresh chopped parsley and serve warm. Enjoy!