Add the sliced pears and grated ginger to the slow cooker. Sprinkle the brown sugar and cinnamon over the fruit and stir gently to coat.
In a bowl, combine the rolled oats, flour, and melted butter until the mixture forms loose clumps. Scatter this topping evenly over the pears.
Cover and cook on low for 3 hours, until the pears are soft but still hold their shape and the topping is lightly golden at the edges.
While the crumble cooks, whisk together the milk, granulated sugar, cornstarch, and vanilla extract in a small saucepan. Heat over medium, stirring constantly, until the mixture thickens into a smooth custard. Remove from heat.
Spoon the warm crumble into bowls and pour the vanilla custard over each serving.