Preheat the oven to 300˚. In a blender, puree the raspberries with the brown sugar and hot water until well combined. Strain through a fine mesh sieve into a medium bowl and discard the seeds. Stir in the rhubarb, butter and vanilla.
Transfer the sauce to a 9-by-9-inch baking dish and bake, uncovered, stirring every 10 minutes to ensure even cooking, until the rhubarb is soft and sweet, about 40 minutes.
Let the rhubarb cool for 10 minutes before serving over ice cream (and/or shortbread cookies, biscotti, etc.) if desired.
The rhubarb sauce can be refrigerated for up to 4 days.