In a small saucepan combine the rhubarb, sugar, and lemon juice. Place over medium heat, stirring occasionally, until rhubarb releases its juices and begins to break down, about 5 minutes. Continue cooking (and stirring) until rhubarb has thickened and reduced by nearly half, about another 5 minutes. Remove from heat and set aside to cool while preparing the rest of the bars.
For the oat crust:
Preheat oven to 350 degrees. Line a 9x9 square baking pan with parchment paper and lightly coat with baking spray, set aside.
Whisk together the flour, oats, brown sugar, and salt until combined. Pour in the melted butter and mix to form a crumbly dough. Press into the bottom of the prepared pan and bake in preheated oven for 10 – 12 minutes, or until edges are lightly browned.
Remove from oven and allow to cool on wire rack while you prepare the cheesecake filling.
For the cheesecake filling:
In the bowl of a stand mixer cream together the softened cream cheese and sugar until light and fluffy, about five minutes, scraping down the sides of the bowl as necessary. Add in the half & half, egg, and vanilla, mixing until smooth and once again scraping down the sides and bottom of the bowl to be sure mixture is even and smooth. Pour into prebaked crust.
For the rhubarb compote swirl: Place small spoonfuls of cooled compote around the cheesecake batter. Swirl with a chopstick or butter knife to incorporate slightly.
Bake cheesecake bars in preheated oven for 20 – 25 minutes, or until edges are golden and center just barely jiggles.
Remove from oven and cool completely on wire rack before chilling in fridge for at least four hours, or overnight.
When ready to serve, lift the cheesecake out of the pan using the parchment paper as handles. Run a sharp knife under a hot water and evenly slice cheesecake into 16 squares.
*Bars can be kept, covered, in the fridge for up to five days.