In a large saucepan over high heat, combine the rhubarb, sugar and 2 tablespoons of water. Bring to a boil, then reduce heat and simmer, stirring frequently, until the rhubarb is tender and falling apart, about 10 minutes. In a small bowl, whisk the cornstarch and 1/2 cup water until smooth. Off the heat, gradually pour the cornstarch mixture into the hot rhubarb mixture, whisking continuously. Bring the mixture to a boil over medium-high heat and cook, stirring continuously until thickened, about 3-5 minutes. Stir in red food coloring if using. Cool completely.
In the bowl of a food processor, blend the brown sugar and graham crackers until finely ground. Add melted butter and process until well combined. Press into the bottom of a 9-inch springform pan. Using the bottom of a juice glass, press the crust evenly and firmly into the pan.
In the bowl of an electric mixer, beat the cream cheese, sugar and vanilla until smooth. Add the eggs one at a time, beating after each addition. Beat in the yogurt until smooth and fluffy.
Pour about 2/3 of the cheesecake batter into the prepared crust. Reserving about 1/2 cup of the cooled rhubarb compote for the top of the cheesecake, drop dollops of the remaining rhubarb compote onto the surface of the batter, and using a skewer or chopstick, swirl the rhubarb into the batter in circular motions. Be careful not to disturb the crust on the bottom. Pour the remaining cheesecake batter on top and smooth with a spatula until covered.
Bake the cheesecake in a preheated oven for up to 1 hour. Check after 50 minutes to make sure the cheesecake is not browning. Remove from the oven when the center is just set and still a bit jiggly.
Cool completely on a rack and then refrigerate for at lease 6 hours, preferably overnight.
Spread the remaining rhubarb compote on the top of the cheesecake and serve. Or whisk the remaining rhubarb compote into a cup of Green Mountain Creamery Strawberry Yogurt and serve on the side.