In a medium bowl, whisk together the mayonnaise, buttermilk, sour cream, dill weed, parsley, dried chives, onion powder, garlic powder, Worcestershire sauce, salt, and black pepper until smooth. Cover and refrigerate for at least 1 hour to allow the flavors to develop and thicken.
Preheat your oven or air fryer according to the package instructions for the fries, typically 400–425°F. Cook the fries in a single layer for 18–22 minutes, flipping halfway through, until golden brown and crispy.
While the fries cook, heat a large griddle or skillet over high heat and add the oil. Add the diced red bell pepper, green bell pepper, and sweet onion, sautéing for 3–5 minutes until they begin to soften and lightly char, then push them to the side of the griddle.
Place the shaved chicken breast onto the hot surface in an even layer and season with Cajun seasoning. Let it cook undisturbed for 2–3 minutes to develop a crust, then flip and chop into bite-sized pieces, cooking for another 3–4 minutes until fully cooked through and slightly caramelized.
Mix the sautéed peppers and onions back into the chicken and cook together for 1–2 more minutes so the flavors combine. Remove from heat once everything is tender and well mixed.
Transfer the hot fries to a large serving platter and immediately top with shredded pepper jack cheese so it begins to melt. Spoon the chicken and pepper mixture over the fries, sprinkle with crumbled bacon, drizzle generously with the chilled homemade ranch, and finish with fresh chives before serving hot.