Add the peaches to a large high-sided saute pan with the vanilla, 3 tablespoons of the brown sugar and 1/2 teaspoon of the ginger. Cook over medium-high heat until the peaches start to defrost and soften and the sugar starts to melt, about 5 minutes. Pour the peach mixture into a 9-inch deep-dish baking dish and set aside to cool.
In the bowl of a food processor fitted with a blade, mix together the whole-wheat flour, salt, remaining 1/4 cup brown sugar and 2 teaspoons ginger. Add the cold butter to the food processor and process until it starts to come together to form a dough. Add the pecans and oats and pulse just until the pecans are roughly chopped.
Crumble the crumb topping onto the peaches, coating them completely. Bake until the peaches are tender and the crumble is golden brown, 45 to 50 minutes.
Serve the crumble with vanilla ice cream and spoon over the Buttered Pecan Ice Cream Topping.
Buttered Pecan Ice Cream Topping:
In a small saucepan, combine the butter, sugar, corn syrup and salt. Cook over medium heat, stirring constantly, until the sugar is melted and the mixture becomes thick and syrupy, 2 to 3 minutes. Stir in the pecans, then remove from the heat and stir in the vanilla. Let cool slightly.