Preheat the griddle or skillet on medium heat. For griddle cooking, the griddle temperature should be about 400-425℉.
Slice your ribeye steaks as thinly as possible against the grain, then roughly chop into smaller pieces.
Add about 1 tablespoon of oil to the heated griddle surface and spread it around with your spatula. Sauté the diced bell peppers and onions on the oiled surface until tender. When vegetables are about ¾ of the way cooked through, season with all-purpose seasoning or salt and pepper, and move to the cooler side of the griddle to make room for the steak.
Add the chopped ribeye to the griddle to cook. Season with all-purpose seasoning. Cook the steak until almost done to your liking. Then, mix the steak and vegetables together on the griddle. Continue to cook until steak is done to your liking.
Remove the steak and vegetable mixture from the griddle and transfer to a large bowl. Allow to cool slightly, and then mix in about ¼ of the shredded cheese.
Assemble the taquitos. Warm your corn tortillas on the griddle just until they’re pliable. Then, add a spoonful of the cheesesteak mixture to one side of the warm tortilla, and spread about 2-3 tablespoons of shredded cheese on the other side. Roll up tightly so that the cheese is on the seam side - as the cheese melts it will help seal the seam.
Add a small bit of oil to the heated griddle. Place the taquito seam side down in the oil. *TIP - When you place the taquito on the griddle, use your spatula to apply a bit of pressure for about 10 seconds so that the cheese melts a bit to seal the seam. This helps your taquito to not come unrolled. Repeat for the remaining taquitos.
When the taquitos have a nice golden color on the first side, add more oil to the griddle if needed, and roll to the next side. Continue cooking and rotating the taquitos until crispy and golden brown on all sides. As the taquitos finish cooking, transfer to a wire rack or paper towels to drain off excess oil.
Serve cheesesteak taquitos with cheese sauce for dipping.