For the bread: Preheat the grill to 400 degrees F.
Lay out the dough on a work surface and sprinkle with the olive oil, parsley, rosemary, garlic, a pinch of salt and a few grinds of pepper. Fold it over itself and roll out or just press with your hands to make a square that could fit four slices of bread, because that's the goal. (You will eventually want to cut this into fourths to serve.) Place on the direct heat of the grill and cook until it releases from the grill and is slightly golden brown, 3 to 5 minutes. Flip and cook until done, 5 to 8 minutes.
For the bacon: Mix the brown sugar, cayenne pepper, zest and a few grinds of black pepper in a bowl. Press the bacon into this mixture and place on a piece of nonstick aluminum foil on the grill. Cook, without flipping, until the bacon is crispy, 18 to 20 minutes. Remove from the grill and roughly chop.
For the tomatoes and lettuce: Brush the tomato slices and lettuce with olive oil and sprinkle with a pinch of salt and pepper. Place the tomatoes and lettuce directly on the grill and cook, flipping halfway through, until the tomatoes and lettuce are slightly charred, 3 to 5 minutes.
Build the sandwiches: Mix the mayonnaise, honey, lemon juice and sriracha seasoning in a small bowl. Chop the grilled tomatoes and lettuce. Add the chopped tomatoes to the bread and press them slightly into the bread, then add the chopped bacon and piles of lettuce. Drizzle with the sriracha mayonnaise. Cut into four pieces and serve.