Heat the olive oil in a skillet over medium heat. Add the thinly sliced red onion half-moons and cook for 5 minutes, stirring occasionally until they begin to soften. Add the sugar and apple cider vinegar, then reduce heat to low and cook for another 5-10 minutes, stirring frequently, until the onions are deeply caramelized and jammy. Season with a pinch of salt. Transfer to a bowl and set aside—these can stay at room temperature while you prepare the rest of the sandwich components.
While the onions cook, combine the mayonnaise, freshly minced garlic, and crushed red pepper flakes in a small bowl and mix until smooth—set aside. Pat the chicken strips dry with paper towels, then season them evenly with the Italian seasoning on both sides. I like to let the seasoned chicken sit for a minute or two so the flavors can start to penetrate the meat.
In the same skillet used for the onions (or a fresh one if needed), heat it over medium-high heat until shimmering. Add the seasoned chicken strips and cook for about 5 minutes on the first side without moving them, allowing them to develop a golden-brown crust. Flip and cook the other side for another 5 minutes until the chicken is cooked through and golden on both sides. Transfer to a plate.
Preheat your oven to 375°F. Place the King's Hawaiian rolls or sub rolls open-faced on a baking sheet. Spread the garlic mayo mixture from Step 2 generously on both halves of each roll. On the bottom half of each roll, layer the spinach first, then the cooked chicken strips from Step 3, followed by the caramelized red onions from Step 1, and finally top with a slice of provolone cheese. For the best result, I like to slightly overlap the cheese so it melts evenly across the sandwich.
Bake the assembled sandwiches in the preheated 375°F oven for 5 minutes, or until the cheese is melted and the buns are warm and slightly toasted. Remove from the oven, place the top halves of the rolls on each sandwich, and serve immediately while the cheese is still warm and gooey.