First, make the glaze by combining the bourbon, sugar, ketchup, Worcestershire sauce, lemon juice and chili with garlic sauce (or Sriracha) in a small pot. Whisk until combined.
Heat the mixture over medium-high heat until it comes to a boil. Take 2 TBS or so of the sauce and place it into a small bowl, add the cornstarch to it, and mix until the cornstarch dissolves.
Carefully scrape all of the mixture back into the pot and continue to boil for 2 minutes, whisking occasionally. Remove from heat. Taste and adjust flavor to your preference and set aside. (Bourbons and whiskies vary in strength and taste, feel free to add more sugar or ketchup, etc. until you achieve the flavor you enjoy best)
Fire up your grill, slice the onion into thin slices and lightly brush with a bit of oil. Season with salt and pepper and grill over med-high heat, moving them around from time to time to prevent charring.
Halfway through, brush the onions with a bit of the Bourbon Glaze. Continue cooking until the onions are done to your liking. Place them in a small bowl and cover with foil until ready to assemble the sandwiches.
On the other side of the grill, cook your sausages. As soon as you take the sausages off of the grill, liberally brush them with Bourbon Glaze.
Assemble sandwiches by splitting the rolls, piling on onions and roasted peppers, then topping with the sausages. Add additional onions and glaze over-top, as well as Parmesan cheese.
Notes: If you are not a huge fan of the taste of Bourbon, start with 1/2 cup - you can add the other 1/4 cup after you have tasted it. Some Bourbons are very strong. Feel free to add greens to your sandwiches as well. Glaze can be made 1-2 days ahead of time and kept in the refrigerator in a sealed jar.