In a large skillet or medium saucepan set over medium heat, melt the butter. Whisk in the brown sugar and flour. Cook, whisking constantly, for about 2 minutes to eliminate the taste of the raw flour.
Pour in the half-and-half and cook, whisking constantly, until the sauce thickens, about 5 minutes. Remove from heat and whisk in rum, fresh lemon juice and vanilla extract. Keep the sauce warm over low heat until ready to use, whisking occasionally.
Preheat grill to medium-high heat. Brush grill with canola oil. Lay the pineapple on the grill and cook, about 5 minutes, turning halfway through cooking.
Remove the pineapple from the heat, and serve with ice cream and the brown sugar rum sauce.
From the kitchen of Cookin' Canuck | cookincanuck.com