Preheat oven to 400°. Peel bananas, and cut into 1/2-inch slices. Place in a 2-qt. baking dish, and sprinkle with light brown sugar and butter. Bake 20 minutes, stirring halfway through. Let cool 30 minutes. Gently mash into chunks.
Whisk together granular sweetener, cornstarch, and salt in a large heavy saucepan. Gradually whisk in milk and half-and-half. Cook over medium heat, stirring constantly, 8 to 10 minutes or until mixture thickens slightly. Remove from heat.
Whisk egg yolk until slightly thickened. Gradually whisk about 1 cup hot cream mixture into yolk. Add yolk mixture to remaining cream mixture, whisking constantly. Whisk in vanilla.
Pour mixture through a fine wire-mesh strainer into a bowl, discarding solids. Cool 1 hour, stirring occasionally. Place plastic wrap directly on cream mixture; chill 8 to 24 hours.
Pour mixture into freezer container of a 1 1/2-qt. electric ice-cream maker, and freeze according to manufacturer's instructions; stir in bananas and crushed vanilla wafers halfway through freezing. Let stand at room temperature 5 to 10 minutes before serving.
*Granulated sugar may be substituted.
Note: We tested with Whey Low 100% All Natural Granular Sweetener for Ice Cream. Get 20% off any time you order from wheylow.com. Coupon code: SouthrnLvg