Start by making the teriyaki sauce. Combine all ingredients and bring to low simmer on stovetop. Let simmer for about 15min. The mixture will reduce and thicken slightly but it won't be thick like A1 sauce. Pour finished teriyaki sauce in another container and let it cool to room temp.
While the teriyaki sauce is simmering, toss the poblano peppers in olive oil and salt/pepper. Roast the poblano peppers in the oven at 400F, turning every 8-10 min. Let roast in oven until skin blisters and darkens (15-20min). Once done, let the peppers cool to the touch, remove the seeds and the outer blistered skin, then dice the peppers.
Hand mix the ground chuck, hot Italian sausage, and diced roasted poblano peppers. Shape into 8 evenly sized patties. Grill patties until done. Melt a slice of cheese over each patty just before removing from the grill.
Toast the buns cut side down on the grill until slightly browned. Time to assemble!
Slather about 1 Tbsp of cooled teriyaki sauce onto the top and bottom bun. Layer the burger starting with the bottom bun, romaine lettuce leaf, burger patty with melted cheese, another romaine lettuce leaf, then top bun.
Note: For a spicier version, leave all of the seeds from the poblano peppers in the mixture.