Cover a large, rimmed sheet pan with aluminum foil. Spread half of the olive oil evenly out over the foil. Set aside.
Add the prepared peppers & onions to a large mixing bowl.
Add the spices to a small mixing bowl & whisk together to evenly combine.
Sprinkle half of the spice mix over the veggies, and then toss them to coat. Sprinkle half the Worcestershire out over top, and gently toss again to evenly coat.
Transfer the seasoned vegetable mixture to the prepared sheet pan. Spread the mixture out evenly to cover all of the pan.
Add the chicken to the previously used large mixing bowl. Sprinkle the rest of the seasoning blend over top and toss to coat. Sprinkle the rest of the Worcestershire out over top, and toss again to evenly coat.
Using a pair of tongs, set all of the chicken pieces on top of the veggies- spacing them out evenly as you go.
Bake the chicken & vegetables at 375° for 15-17 minutes.
While that bakes, shred the cheese sticks into thin strips. Set aside.
When the chicken & veggies have finished baking, carefully remove the pan from the oven. Spread the cheese strips evenly out over top.
Return the sheet pan to the oven, and broil- watching carefully, until the cheese is melted and beginning to turn golden brown in spots. Carefully remove the pan from the oven, and set aside.
On another sheet pan, add halved hoagie rolls (upright position). You should be able to fit four at a time.
Spread mayo on the insides of the rolls (both sides) in a thin layer.
Using a spatula, transfer 1/4 of the prepared chicken & veggie mixture to the bottom half of one of the prepared hoagie rolls. Repeat until all the mixture's been evenly divided between the remaining rolls.
Top each with two slices of provolone cheese.
Return the sheet pan to the oven, and broil again (watching carefully) until the cheese is melted and the buns are lightly toasted.
Working carefully, transfer the cooked sandwiches to waiting plates. Serve them as is, or top with your desired toppings first. Enjoy!