In a skillet over medium-low heat, add 2 teaspoons vegetable oil and the onion. Caramelize for about 10 minutes. Add peppers and carrot and cook until softened, about 7 minutes. Stir in the Kikkoman® Stir-Fry Sauce and cook for 3 more minutes, then remove from heat.
On a griddle or other flat-top cooking surface over medium-high heat, place open hoagie rolls middle side down. Drizzle 2 teaspoons oil on another part of the surface and add the beef. Using tongs or spatulas, shred the beef into smaller pieces. Add the cooked peppers and onion and continue tossing the mixture into the beef until beef is cooked.
Divide into 4 sections and add 2 slices provolone to each section. Lift each section and place in a hoagie bun. Top with hot peppers if desired.