Heat olive oil in a large skillet over medium heat. Season chicken with blackened seasoning and cook until mostly cooked through, flipping once (about 5-6 minutes).
Scoot chicken to the side of the pan. Add 2 tablespoons butter and 3 cloves minced garlic. Toss chicken in the garlic butter, then transfer to a bowl and tent with foil.
In the same pan, over medium-low add 5 tablespoons butter, half and half, heavy cream, Cajun seasoning, salt, and pepper. Bring to a low gentle boil for 5 minutes, whisking frequently.
Stir in parmesan cheese and cook until melted and thickened. Remove from heat and set aside. It will continue to thicken as it cools.
Preheat oven broiler. Split slider buns and place cut-side up on a baking sheet.
Mix melted butter, garlic, and parsley. Spread half on the inside of the buns and broil until golden.
Preheat oven to 375°F.
Sprinkle ¾ cup Monterey Jack on bottom buns. Add chicken, bacon, remaining cheese, and spoon alfredo sauce evenly over top.
Place top buns on, spread remaining garlic butter over tops, and bake for 20 minutes, tenting with foil to prevent the tops from browning too quickly.
Slice and serve warm with extra alfredo sauce for dipping.