Place cherries in a large bowl. Add 1/2 cup Grand Marnier + 2 tablespoons sugar. Stir, cover, and chill for at least 30 minutes, stirring periodically.
Pour the cherries and all the liquid into a large skillet or saucepan over medium-low heat. Cook the cherries, stirring frequently, until they're very soft and the liquid has reduced and thickened, approximately 15 minutes. Allow the mixture to cool briefly and then puree in a blender. For some texture in the ice cream, don't puree the cherries completely.
Heat the cream, half & half, and vanilla in a medium-sized saucepan over medium-high heat. In a medium-sized bowl, whisk together the egg yolks and 1/3 cup sugar. When the cream begins to simmer, turn the heat to low and ladle half of it into the egg mixture while whisking. Pour the mixture back into the saucepan, using a spatula to get everything out of the bowl. Using a heatproof spatula or wooden spoon, stir the custard over low heat until it thickens up a bit and coats the back of spatula. Stir in the cherry mixture.
Allow the mixture to cool for several minutes, stirring periodically. Take a small taste and if you feel that it needs more Grand Marnier flavor, stir in an additional 1-2 tablespoons. Pour the liquid into a bowl and cover with plastic wrap, pressing the plastic directly against the liquid to prevent a skin from forming. Chill until very cold, preferably overnight.
Prepare the ice cream in a machine according to manufacturer's instructions.