To make the crumble topping:.
In a stand mixer using the paddle attachment, combine the flour, oatmeal, brown sugar, and salt. Add the cold butter and mix on low speed until the topping just begins to come together and resembles large bits of chunky dough. (Do not mix so long that it comes together completely.) Transfer the topping to a shallow container, breaking it up a bit. Cover and refrigerate for at least 2 hours.
To make the filling:.
Heat the oven to 350 degrees F. Combine the pears, cranberries, lemon juice, vanilla, cinnamon, nutmeg, sugar, salt, and flour. Toss the ingredients lightly to coat evenly and pour into a 1 1/2-quart baking dish. Top with the crumble topping, breaking up any large clumps with your fingers and spreading it evenly. At this point, there may be areas that aren’t completely covered with topping, but don’t worry because it will spread a bit as it bakes.
Bake until the topping begins to brown and the filling is bubbling, about 40 minutes. Remove the crumble from the oven and let it cool somewhat before serving.