Prepare the griddle. Heat griddle to about 400-425℉.
Prepare the cheese sauce. While griddle is heating, pour the heavy cream into a small saucepan on the griddle. Heat cream until just about boiling, then add cheddar and American cheese. Stir frequently as cheese is melting into the cream. Continue to cook until cheese sauce reaches desired consistency, keeping in mind that it will thicken as it cools. If needed, add more heavy cream or more shredded cheese.
Portion beef. Roll ground beef into loosely packed balls that weigh about 4 ounces each. You can use a ½ cup measuring cup to portion out the beef if you wish.
Sauté the vegetables. Add the sliced peppers and onions to the hot griddle surface and sauté until tender. Then move to the cooler side of the griddle to keep warm.
Smash the cheesesteak tacos. Place a ground beef ball on the hot griddle surface and sprinkle with salt and pepper. Then place one flour tortilla over the beef ball, and use a burger press to smash the beef onto the griddle. The flour tortilla should be in between the beef ball and the burger press. After smashing, apply even pressure for about 10-15 seconds to ensure a good crust.
Flip the cheesesteak tacos. After about 2 minutes, or when you think the burger is mostly cooked through, use your griddle spatula to flip to the second side to continue to cook. Take care to scrape underneath the burger crust, so that all of that delicious flavor isn’t left behind on your griddle surface.
Add the cheese. Top the smashed beef patty with a spoonful of cheese sauce or a slice of cheese and the sautéed onions and peppers. Continue to cook until the cheese is melted and the tortilla is slightly crispy and golden brown.
Serve. When the cheesesteak tacos are done cooking, transfer to a serving platter to rest and cool for about 4-5 minutes. Then serve with your favorite cheesesteak toppings.