In a large bowl, combine ground beef, jerk seasoning, smoked paprika, cilantro, garlic, and pepper. Mix together and form beef into burger patties then sprinkle with salt. (I made 4 half pound burger patties but feel free to scale up or down on the size)
Slice a red onion. Set aside. Slice a pineapple to make 4-5 slices and dust each slice with cinnamon. Set aside.
Heat olive oil in a skillet and add burger patties. Cook until desired doneness and remove from skillet. Add red onions and saute for about 5 minutes, until onions begin to soften and caramelize. Remove and side aside.
Add pineapples to the skillet and cook on each side for 4-5 minutes, until slightly blackened on each side.
Cut a brioche bun in half and spread mayo onto both slices. Assemble burger by adding the grilled pineapple on the bottom, then the burger patty, colby jack cheese, red onions and arugula.