Preheat the oven to 350. Lightly grease a 9x9 baking dish.
In a large mixing bowl, toss together the chopped rhubarb, white sugar, brown sugar, cornstarch, salt and vanilla until well combined. Pour into the baking dish.
In another mixing bowl, combine the flour, brown sugar, rolled oats and quick cooking oats. Cut in the butter slices, until little crumbles form. Sprinkle the topping all over the rhubarb in the baking dish.
Bake in the preheated oven for about 50 minutes, or until rhubarb and sauce is bubbly and thick, and topping is golden brown.
Serve Rhubarb Crisp with vanilla ice cream, or whipped cream topping.