Preheat the Griddle: Heat your griddle to 375–400°F.
Start the Sausages: Place the sausages directly on the griddle as it preheats. If you have a dome, cover the sausages to help them cook through evenly.
Cook the Veggies: Add oil to the griddle, then toss on the sliced peppers and onions. Cook alongside the sausages, stirring the veggies occasionally.
Warm the Marinara: Pour marinara into a small sauce pot and place it on a cool zone or corner of the griddle. If it starts bubbling too hard, move it to a wire rack to keep it warm without boiling.
Turn the Sausages: Rotate the sausages every few minutes until browned on all sides and cooked to an internal temperature of 160°F.
Season the Veggies: Add salt, pepper, vinegar, and sugar to the peppers and onions. Toss until the seasoning forms a light glaze or sauce.
Build the Sandwich Base: Divide the veggie mix into 5 piles, roughly the length of your buns. Top each pile with 2 slices of cheese and squirt a bit of water near them to help the cheese melt. Cover with a dome if you’d like.
Assemble the Sandwich: Place a sausage on top of each cheesy veggie pile. Then place your toasted bun directly over the sausage.
Flip and Finish: Slide your spatula under the veggies while holding the bun in place with your hand. Flip the whole thing upright so the bun is on the bottom. Spoon warm marinara over the sausage and serve hot.