To make the filling, combine the rhubarb and white sugar in a saucepan. Cook over medium heat, stirring occasionally, until the rhubarb has broken down and is soupy, about 10 minutes.
Stir the cornstarch into the water to make a slurry, then stir that into the rhubarb mixture. Bring the mixture to a boil and cook, stirring occasionally, just until thick, 1 to 2 minutes. Remove from the heat and stir in the vanilla extract.
Preheat the oven to 350 F and butter a 9 by 13 inch baking pan.
To make the crust and topping, put the oats, flour, brown sugar, walnuts, baking soda, and salt in a medium bowl and stir to combine. Add the butter and use your fingers to work it in until the mixture is crumbly.
To assemble and bake the bars, transfer half of the mixture to the prepared pan and press it evenly across the bottom. Scoop ricotta over the crust and using the back of a spoon spread it evenly across. Pour over the rhubarb filling and spread it in an even layer. Sprinkle clumps of the remaining oat mixture over the filling.
Bake for 30-35 minutes, until bubbling and golden brown.
Let cool completely before cutting and serving.