1. Preheat oven to 350ºF. Butter an 8-inch square baking dish. Combine gingersnaps, pecans, flour and brown sugar in bowl of a food processor and pulse several times to coarsely chop cookies and pecans. Add butter and process until clumps begin to form.
2. Arrange peaches, cut side up, in baking dish. Press cookie mixture into center of each peach, pressing to adhere. Bake until peaches are tender and topping is browned, about 30 minutes. Let stand 10 minutes to cool slightly.
3. While peaches are cooling, whip cream with sugar until stiff peaks form. Transfer peaches to dessert bowls and serve with whipped cream.