Add butter, brown sugar, rum, orange juice, cinnamon, vanilla extract and salt to a medium sized pan over medium high heat.
Allow sauce to melt together then stir until combined. Bring sauce to simmer and allow sauce to reduce by about a ⅓.
Add pineapple rings to a glass dish and pour ¾ of the sauce over the pineapple. Leave the rest for serving.
Allow sauce to soak into pineapple for about 20 minutes, flipping over halfway through at 10 minutes.
While pineapple soaks prepare your grill. Spray grill with non-stick spray or lightly brush grates with oil.
Grill pineapple about 5-7 minutes on each side until beautiful grill marks appear and the pineapple is tender. While grilling, you can baste with additional sauce used for soaking the pineapple.
For the Doughnuts:
Spray the grill again or add oil again. Add doughnuts to the grill and carefully watch because they can burn fast. Grill for about 20-40 seconds then flip to grill the other side. Serve immediately warm.
To prepare sundaes, cut a donut in half, add pineapple slice and top with ice cream and leftover sauce (keep warm) and serve.