For the sauce: Whisk the water and arrowroot powder together and place in a saucepan. Add the rest of the sauce ingredients and turn the heat to medium-low. Whisk the sauce until it has slightly thickened, then remove from heat.
In a large mixing bowl, mix the ingredients for the burgers together until well-combined.
Divide into four equal portions and form the meat into burger patties.
Pre-heat a grill to medium-high heat.
Place the burgers and pineapples on the grill when it becomes hot and close the lid. Do not place the pineapples over direct flame.
Cook for 5 minutes on each side, or until burger is cooked to your liking.
Top the burgers with some of the sauce and the grilled pineapples.
Serve on lettuce buns, or eat with a fork and knife! Enjoy!