Divide the ground chicken into four equal portions, about 4 ounces each, and shape them into patties.
Season one side of each patty generously with Cajun or blackened seasoning.
Place the patties on the hot griddle, seasoned side down, and press gently with a spatula to create a seared crust.
Season the top sides of the patties, then flip them after a few minutes to continue cooking.
In a small bowl, combine mayonnaise, chopped parsley, juice from half a lemon, Cajun hot sauce to taste, and Cajun or blackened seasoning to taste. Stir until well mixed and set aside.
Drizzle cooking oil on the griddle and add the diced garlic, sweet pepper, and jalapeño. Stir occasionally as they cook until softened.
When the patties are nearly cooked through, place one slice of pepper jack cheese and one slice of sharp cheddar cheese on each patty.
Top the cheese with a spoonful of the cooked garlic and pepper mixture.
If needed, spray a little water onto the griddle and cover the patties with a basting dome or the griddle hood to help melt the cheese.
Butter the cut sides of the brioche buns and place them butter-side down on the griddle. Toast until golden brown and remove from the griddle.
Spread Cajun mayo on the bottom half of each toasted bun.
Place a leaf of butter lettuce on top of the mayo.
Add a cooked patty with melted cheese and peppers on top of the lettuce.
Spread more Cajun mayo on the top half of the bun if desired and place it on top to finish the burger.
