In a small bowl, whisk together mayonnaise, minced garlic, lemon juice, and a pinch of salt. Cover and chill until ready to serve.

Heat 1 tbsp olive oil in a large skillet over medium-high heat. Add peppers and onions; sauté until soft and slightly caramelized, about 5–6 minutes. Transfer veggies to a plate.

Add remaining olive oil to the skillet. Season the ribeye slices with salt and pepper, then cook until just browned, about 3–4 minutes. Return veggies to the pan and toss to combine.

Reduce heat to low. Layer mozzarella over the steak-and-pepper mixture; cover the skillet and let cheese melt, about 2 minutes.

Meanwhile, split hoagie rolls and toast lightly under the broiler or in a toaster.

Spread garlic mayo generously inside each roll. Divide the cheesesteak filling among the rolls.

Serve hot, garnished with extra pepper relish or pickle slices if desired.