Melt butter in a medium sauce pan or skillet. Stir in brown sugar. Cook for ~2-3 minutes on medium low heat.
Add cherries and a pinch of salt. Simmer for roughly 10 minutes, stirring occasionally. The cherries will release a lot of liquid. Add bourbon or orange juice. Cook for another 1 minute. Add lemon juice to your preference.
Stir cornstarch mixture into the cooked cherries, mixing well to get even thickening. Simmer for about 2-3 minutes to cook out the raw cornstarch flavor. Remove from heat and let the cherries jubilee cool to room temperature or refrigerate. The cherries need to be cold when folding into the ice cream.
No Churn Vanilla Ice Cream, adapted from Martha Stewart
In a small bowl or measuring cup, mix condensed milk, bourbon, and vanilla extract together. Set aside.
In a large bowl, whip cold heavy cream until stiff peaks form, ~2-3 minutes if using an electric mixer.
Take 1/3 of the whipped cream and stir into the sweetened condensed milk. No need to be so gentle in this step. This is to lighten the condensed milk to make the folding easier in the next step.
Take the lightened condensed milk mixture and gently fold into the remaining whipped cream, with a spatula. Fold as gently and thoroughly as you possibly can without deflating the whipped cream too much. A few streaks are ok.
Final assembly :
In a loaf pan or quart-size food container (you will need 2, most likely), gently fold cherries into the cream mixture, creating ripples of cherries through out container, but don't completely blend in the cherries jubilee.
Freeze for at least 4 hours. For frozen hard ice cream, let the ice cream soften in the refrigerator for about 30-45 minutes before serving.