Prep the chicken. Slice chicken very thin, about 1/4 inch. Pat dry and season with salt, pepper, and smoked paprika.
This helps quick browning and big flavor.
Slice the veggies. Cut onions and peppers into thin strips. Mince the garlic. Keep everything ready by the stove—this moves fast.
Toast the rolls. Split hoagie rolls and lightly toast cut-side down in a dry skillet or under the broiler until just crisp.
Set aside.
Sauté the veggies. Heat 1 tablespoon oil in a large skillet over medium-high. Add onions and peppers with a pinch of salt. Cook 6–8 minutes, stirring now and then, until softened and golden at the edges.
Add garlic for the last minute. Transfer to a plate.
Cook the chicken. Add the remaining oil to the skillet. Increase heat to high.
Add chicken in a single layer. Let it sear undisturbed for 2 minutes, then stir and cook another 3–4 minutes until cooked through and lightly browned.
Sauce it up. Reduce heat to medium. Return veggies to the skillet with the chicken.
Pour in 3/4 cup BBQ sauce and toss to coat. Simmer 1–2 minutes to thicken slightly. Taste and add more sauce if you want it saucier.
Cheese melt. Pat the mixture into hoagie-length mounds in the skillet.
Lay cheese over each mound. Cover for 30–60 seconds until melted and gooey.
Assemble. Use a spatula to scoop each cheesy mound into a toasted roll. Press gently to set.
If you like heat, add jalapeños or a shot of hot sauce.
Serve. Eat hot with napkins on standby. These are messy—in the best way.