Preheat an outdoor grill or stove-top grill pan over medium-high heat.
Place the butter in a heat-safe ramekin or small skillet and set on the hot grill. Cook, stirring often, until the butter has browned, about 8 to 10 minutes. Remove and allow to cool slightly. Note: If making this indoors with a stove-top grill pan, just brown the butter in a skillet on the stove over low heat.
To make the streusel, combine the flour, granulated sugar, brown sugar, salt, cinnamon, ginger, and nutmeg in a medium bowl. Add 4 tablespoons of the browned butter and stir until the mixture resembles coarse crumbs. Stir in the oats and nuts, if using. Cut a large piece of aluminum foil, fold it in half and then crimp the edges up to create a make-shift dish. Transfer the streusel to the foil and spread out evenly. Set aside.
Brush the sliced peaches and pineapple on both sides with the remaining browned butter, saving some for when the fruit finishes cooking.
Place the foil with the streusel on one side of the hot grill. On the other side, arrange the fruit in a single layer. Cook until the fruit develops grill marks and softens slightly, about 3 to 4 minutes per side. Cook the streusel, stirring often, until golden brown, about 8 to 10 minutes. Remove the fruit and streusel from the grill. Brush the fruit with the remaining browned butter. Allow streusel and fruit to cool slightly. Once cooled, slice the fruit into large chunks.
To assemble the sundaes, scoop the ice cream into individual serving dishes. Top each with fruit, whipped cream and streusel. Serve immediately and enjoy!