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. Note: If making this indoors with a stove-top grill pan, just brown the butter in a skillet on the stove over low heat. Remove and allow to cool slightly.
To make the streusel, in a medium bowl, combine the flour, granulated sugar, brown sugar, salt, cinnamon, ginger, and nutmeg. 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. Transfer the fruit and streusel onto a baking sheet or platter. Brush the fruit with the remaining browned butter, pour the streusel into a dish and set both aside 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!