To make the sauce, stir together the mayo, teriyaki sauce, honey, and cayenne. Set aside.
Griddle the pineapple and bell pepper rings in a skillet over medium-high heat until they have great grill marks. Set aside and add the spam slices to the pan until they have grill marks on each side.
Cook the burgers over medium heat for 4 to 5 minutes on the first side, then flip them over and add a teaspoon of teriyaki sauce on top of each one. Place a slice of cheese on each burger and let it melt while the burger cooks through, about 4 minutes longer.
Separate and toast the brioche bun halves either in the toaster or under the grill. Once lightly charred, remove and start stacking the burgers with cheese, spam, burger sauce, red pepper slices, red onion, lettuce, and pineapple inside the buns. Serve with extra burger sauce on the side.