Preheat the oven to 375°F. Grease an 8x8-inch baking dish.
Peel, core and thinly slice the pears. Place them in the prepared dish and sprinkle with the brown sugar, cinnamon and nutmeg. Gently toss to coat and set aside.
Add the oats, flour, brown sugar, softened unsalted butter and cinnamon to a medium mixing bowl. Use your hands to work in the butter until well combined and the mixture resembles moist crumbs.
Sprinkle the topping evenly over the pears without pressing it down. Bake for about 40 minutes, until the top is golden brown, the edges are bubbling and the pears are tender. If the topping browns before the pears are tender, loosely cover with foil and continue baking.
Near the end of baking, combine the caramel ingredients in a medium saucepan over medium heat. Cook, whisking constantly, for about 5 minutes, until the butter is fully melted and the mixture begins to boil lightly.
Continue whisking and allow the sauce to boil gently for another 2 to 3 minutes, until smooth and slightly thickened. Remove from the heat and set aside.
Serve the pear crisp warm with vanilla ice cream or whipped cream, if desired, and the homemade caramel sauce.