Add the maple syrup, half & half, eggs, brown sugar, cornstarch, and salt to a medium saucepan and whisk all of the ingredients together until completely combined.

Heat over medium-low heat and whisk (almost continuously) until the custard is thick like a pudding. This step may take 20 minutes (or even longer depending on your stovetop). When the custard is thick, remove from the heat and whisk in the vanilla extract and butter. Continue whisking until the butter is melted.

Transfer the pudding to a serving bowl or individual dishes and place a piece of plastic wrap or wax paper directly on top of the pudding (to keep a skin from forming). Chill completely before serving.