Preheat the griddle with one side set to medium heat and the other to medium-high heat, approximately 375–400°F.
Remove the stems from the portobello mushrooms.
Use a spoon to gently scrape the dark gills from the underside of each mushroom cap. This creates more room for the cheesesteak filling and helps reduce excess dark mushroom liquid.
Brush both sides of the mushroom caps lightly with neutral oil. Season with kosher salt and black pepper.
Place the mushrooms rounded-side down on the medium-heat section of the griddle.
Cook for approximately 4–5 minutes, until the mushrooms begin to soften and develop some browning.
Flip the mushrooms so the cavity side is against the griddle.
Continue cooking for another 3–4 minutes, allowing additional moisture to cook out.
Remove the mushrooms once they are tender but still firm enough to hold the filling. Transfer them cavity-side up to a broiler-safe sheet pan.
Add approximately 1 tablespoon neutral oil to the medium section of the griddle.
Add the diced yellow onion and red bell pepper.
Season lightly with some of the kosher salt and cook for approximately 5–7 minutes, tossing occasionally, until the onion is tender and the red bell pepper has softened and developed some browned edges.
Move the cooked onions and red peppers to a cooler section of the griddle.
Spread the thin-sliced ribeye across the hotter section of the griddle in a fairly thin layer.
Season the ribeye with the remaining kosher salt and black pepper.
Let the ribeye sear undisturbed for approximately 60–90 seconds.
Use two metal spatulas to turn, separate, and begin chopping the ribeye.
Continue cooking for approximately 2–3 minutes, or until the steak is browned and cooked through.
Bring the cooked onions and red bell peppers back into the ribeye.
Add 1 tablespoon A1 steak sauce to the steak and vegetables.
Using both griddle spatulas, chop the cooked ribeye, onions, and red peppers together into smaller pieces. The mixture should be finely chopped enough to fit neatly inside the portobello caps while still keeping recognizable pieces of steak and vegetables.
Toss the chopped cheesesteak mixture together until the A1 is evenly distributed, then remove it from the heat.
In a small bowl, combine the mayonnaise, 2 tablespoons A1 steak sauce, and black pepper. Stir until smooth and creamy.
Spread approximately 1–2 teaspoons of A1 steakhouse mayo inside each cooked portobello cap.
Divide the chopped ribeye, onion, and red pepper mixture evenly among the six mushroom caps.
Gently pack the filling into each mushroom so the caps are generously filled without piling the mixture so high that it falls off.
Place one slice of provolone cheese over each stuffed mushroom. Fold the cheese slightly if necessary so it follows the shape of the mushroom cap.
Preheat the oven broiler to high.
Place the sheet pan approximately 5–6 inches below the broiler.
Broil for approximately 1–3 minutes, watching continuously, until the provolone is completely melted and develops a few lightly browned spots.
Remove the mushrooms from the oven immediately once the cheese is melted.
Allow the stuffed mushrooms to rest for approximately 3–5 minutes before serving.
Serve warm with additional A1 steakhouse mayo on the side if desired.